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asked Jan 29, 2018 in Mathematics by sforrest072 ( 128k points) INFORMATION FINDING GCF USING PRIME FACTORIZATION. I'll get my scratch paper out for this. Factors: The numbers which are multiplied to get another number. 2. The prime factors of 30 are 2, 3 and 5. For example, the number 15 factors into primes as 3 x 5, and the polynomial x2 - 4 factors as (x - 2)(x + 2). So it is 2 times 3 times 5. If you multiply all primes in the factorization together then 30=2 * 3 * 5. A. It is determined that the prime factors of number 30 are: 2, 3, 5. Continue dividing by 2 until you cannot divide evenly anymore. They act the same as the divisors in a division problem, but in this case, they’re all prime numbers. thevoltreport.com is a channel providing useful Do you need more help? We write number 30 above a 2-column table 2. Can we divide 147 exactly by 2? ... Find the prime factorization of the number 75 answer 5x5x5 . 30=2xx3xx5 Prime Factorization of 30 " " 30 = 2xx15=2xx3xx5 " " Hence , the prime factorization of " "30" " is " "2xx3xx5. The next prime… A prime factorization is equal to a number's prime factors multiplied to equal itself. The prime factorization of 30 will be all the prime numbers you used to divide, in addition to the last result, which is a prime number. prime factorization of 30 This is a topic that many people are looking for. There are different methods which can be utilized to find the prime factorization of a number. 72 = 2 × 2 × 2 × 3 × 3 = 2 3 × 3 2 . And just as a refresher, a prime number is a number that's only divisible by itself and one, so examples of prime numbers-- let me write some numbers down. Finding prime factorization and factor tree. So 75 is equal to 3 times 5 times 5. Please post your question on our S.O.S. Any number where this rule applies can be called a prime factor. Steps to find LCM. Math. Then you take the result from that and divide that by the smallest prime number. ... Prime factorization of 30: 2 × 3 × 5. The GCF of 20, 30 and 105 is 5. Positive Integer factors of 30 = 2, 3, 6, 5, 30 divided by 2, 3, 5, gives no remainder. Prime factors can only have two factors(1 and itself) and only be divisible by those two factors. Prime numbers or primes are natural numbers greater than 1 that are only divisible by 1 and with itself. But if, e.g., the multiplicity of all prime factors of k k k are the same, then the relation (2) can be used. Prime factors of 30 are 2, 3, 5. Next to What is the prime factorization of 32? Advertisement. The numbers 2, 3 and 5 are also the first three prime numbers. 30 is divisible by the prime number 2 which results in 15. Well, this is clearly an odd number. The prime factors of 30 are the prime numbers that can be divided into 30 exactly, with no remainder. 30 equals 2*15. For finding other factors you will start to divide the number starting from 2 and keep on going with dividers increasing until reaching the number that was divided by 2 in the beginning. Steps to find LCM. In addition to the cake method, we can calculate the GCF of two numbers by using the prime factorizations of these numbers.. Once we find the prime factorization of the given numbers by using the factorization tree or the upside-down division method, we can mark the common prime factors.The product of the prime factors is equal to the GCF … What is the prime factorization of 30? This is also known as prime decomposition. Step 5: Multiply all the divisors and remaining prime number (if any) to obtain the LCM. In other words, a composite number is any integer greater than one that is not a prime number. Find the prime factorization of 30 . Prime factorization of 40 using upside down division method. The lcm of 18 and 30 is 90. Let's enter that in. 4. The math and the solutions to prime factorization of 30 is as follows: 30 / 2 = 15 15 / 3 = 5 We can say it's 3 times 25. Use prime factorization to find the LCM of 30 and 40. Prime number are numbers that can divide without remainder, This means that 30 is divisible by 2, 3, 5, numbers. 1. Prime Factors of 30. Because all numbers have a minimum of two factors(one and itself). What is the prime factorization of 73? Use prime factorization to find the LCM of 30 and 40. The prime factors of 30 are 2, 3 and 5. Edited: 3/30/2011 Find the prime factorization of 18 18 = 2 × 3 × 3; Find the prime factorization of 30 30 = 2 × 3 × 5; Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM: LCM = 2 × 3 × 3 × 5; LCM = 90; MathStep (Works offline) 2^5 * 4^2 C. 2^5 * 3 D. 3 * 5^2 I need help please! It is also known as prime decomposition. So the greatest common factor 30 and 50 is 10. Also check out the Least Common Multiple of 30 and 50 Prime factorization or integer factorization of a number is the determination of the set of prime integers which multiply together to give the original integer. What are Factors and Prime Factors? Prime factorization just means finding the prime numbers that multiply to that number. 3 times 25, 25 is 5 times 5. We will now calculate the prime factors of 12 and 30, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12 and 30. Explanation: The Prime Factors for 30 are 2 x 3 x 5 . USING OUR SERVICES YOU AGREE TO OUR USE OF. The process of determining the prime factors of a positive integer is referred to as integer factorization. We have provided the prime factors of the given numbers, such as 24, 12, 30, 100, etc. Since 15 is not a prime number, further division is required, which leads to 15 being divided by 5 equals 3. We write down on the left side of the table the prime factor and next number to factorize on the ride side 4. Use a factor tree to find the prim factorization of 96. We found the factors and prime factorization of 30 and 50. We will provide you with the definition of Factors of 30, show you how to find the Factors of 30, give you all the Factors of 30, tell you how many Factors 30 has, and supply you with all the Factor Pairs of 30 … Step 1: Start with any number that divides 60, in this we will use 10. Prime factorization of 30: By prime factorization of 30 we follow 5 simple steps: 1. In mathematics, factorization (also factorisation in some forms of British English) or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original. We write number 30 above a 2-column table. Look at the numbers going down the left side of the work and the number at the bottom. To get the Prime Factors of 30, you divide 30 by the smallest prime number possible. The Factor Tree of 30 above shows the level of divisions carried out to get the factor numbers. The prime factorization of 30 = 2•3•5. MATH: Home Page. 2^3 * 6^2 B. Finding the prime factors of 30 To find the prime factors, you start by dividing the number by the first prime number, which is 2. List of positive integer factors of 50 that divides 30 without a remainder. Step 4: Continue division until the remainder is a prime number or 1. Use the form below to do your conversion, separate numbers by comma and prime factorization calculator. The prime factorization of 30 is 2 * 3 * 5 Start with the lowest Prime number that will divide into the given number evenly. The prime factorization of 36 is 2 x 2 x 3 x 3. Prime factors of 30 : 2, 3, 5 In number theory, the prime factors of a positive integer are the prime numbers that divide that integer exactly. It is determined that the prime factors of number 30 are: 2, 3, 5. S.O.S. They are integers and prime numbers of 30, they are also called composite number. Use a factor tree to find the prim factorization of 96. Study the tree to see the step by step division. This is because no prime factor of 30... See full answer below. The biggest common factor number is the GCF number. The Prime Factors of 30: 2 • 3 • 5. Greatest Common Factor. How to Find Prime Factorization of a Number. I could have also used other factors to break down 30 … The prime factorization of number 30. using these methods. It's not dividable by 2 evenly that's why we skip it(Remembe 4,5 so you know when to stop later). Trump order on diversity training roils companies. This time, both 2 and 5 are circled because they’re each prime numbers. It works by dividing the starting number 40 with its smallest prime factor(a figure that is only divisible with itself and 1). There are different methods which can be utilized to find the prime factorization of a number. Natural numbers bigger than 1 that are not prime numbers are called composite numbers. Barrymore, Green reunite for 1st time in 15 years 30=2xx3xx5 Prime Factorization of 30 " " 30 = 2xx15=2xx3xx5 " " Hence , the prime factorization of " "30" " is " "2xx3xx5. Prime factorization of 30 in exponential form is: 30 = 2 1 × 3 1 × 5 1 2^5 * 4^2 C. 2^5 * 3 D. 3 * 5^2 I … 3 × 5 = 15. Using prime factorization to find the GCF. Answer link. Prime Factorization:20 = 2 * 2 * 530 = 2 * 3 * 5. Consider d 10 (m) d_{10}(m) d 1 0 (m) for a positive integer m m m. Since 10 = 2 ⋅ 5 10 = 2 \cdot 5 1 0 = 2 ⋅ 5 then Example: Determine the prime factorization of 120. n! Before that, let us discuss what are LCM and HCF in detail. Hence the prime factors of 30 are 2, 3, 5. If there is not a remainder, meaning you can divide evenly, then 2 is a factor of the number. Example: Find prime factorization of 60. And we're done with our prime factorization because now we have all prime numbers here. 1, 2, 5, 10, 25. The prime factorization of 30 is 2 x 3 x 5. Let's do one more of these. The biggest common factor number is the GCF number. 6. ... 60 ÷ 2 = 30 30 ÷ 2 = 15 15 ÷ 3 = 5 5 ÷ 5 = 1 120 = 2 * 2 * 2 * 3 * 5 . Let's try the next prime number, 3: 147 ÷ 3 = 49. If you multiply all primes in the factorization together then 30=2 * 3 * 5. Ultimate Math Solver (Free) Free Algebra Solver ... type anything in there! What is the prime factorization of 33 Work your way up until you arrive to 5 (9 divided by 2, rounded up). You can use prime factorization to find the greatest common factor (GCF) of a set of numbers. We have all the information you will ever need about the Factors of 30. For example 7 has two factors 1 and 7. and k k k, this is easy to compute. 1. Algebra. The prime factorization of 30 is 2 * 3 * 5 Start with the lowest prime number that will divide into the given number evenly. For a printer-friendly version, click here. Now, 73 is interesting. It is simple to factor numbers in a natural numbers set. Learn about prime factorization using our free math solver with step-by-step solutions. Repeat this process until you end up with 1. The answer should be a whole number, and 73½ is not. The prime factorization of a positive integer is a list of the integer's prime factors, together with their multiplicities; the process of determining these factors is called integer factorization. When the bottom numbers on the factor tree are all prime, you have your answer: 30 = 2 × 3 × 5. We could try to factor 73. Write the prime factorization using exponents. Prime number are numbers that can divide without remainder, This means that 24 is divisible by 2, 2, 2, 3, numbers. Use the numbers from the left to write out the prime factorization. 1. PRIME FACTORIZATION = 2 x 3 x 5.When you multiply that you get 30. Creating a factor tree involves breaking up the composite number into factors of the composite number, until all of the numbers are prime. In the last lesson, we found that the prime numbers less than 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.One is usually not counted as a prime number. So this is a prime factorization, but they want us to write our answer using exponential notation. 30 is not a prime number . For example, 2 is on both lists, so we write 2 on a new line. List of positive integer factors of 45 that divides 30 without a remainder. Nine can be divided by 3, now add 3 to your factors. Answer: 2 * 3 * 5 The prime factorization of 30 has 3 prime factors. Cross it out once on each list and write it on a new line. n! 30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49. Amby's Math Resources - Prime Factorization Prime Factorization . Prime Factorization Of 29. Upside down division gives visual clarity when writing it on paper. The number of primes is infinite. It is also known as prime decomposition. Next to What is the prime factorization of 32? If you multiply all the prime factors of 30 you will get 30. In addition to being the factors of 30, the numbers 2, 3 and 5 are also prime numbers, which means that they can only be divided evenly by either the number 1 or by themselves. For example, 24=12•2=6•2•2=3•2•2•2 3•2•2•2 is the prime factorization of 24, since the numbers multiply to 24, and are all prime numbers. Prime Factorization Of 31. To get the number that you are factoring just multiply whatever number in the set of whole numbers with another in the same set. Using prime factorisation method, find the HCF and LCM of 30,72 and 432. 30 divided by 2, 3, 5, gives no remainder. For example, 2, 3 and 5 are the prime factors of 30. Prime factorization of 96 (by division): 96 ÷ 2 = 48 48 ÷ 2 = 24 24 ÷ 2 = 12 12 ÷ 2 = 6 6 ÷ 2 = 3 3 ÷ 3 = 1 The steps are as follows. One way is to repeatedly divide by prime numbers: EXAMPLE 1. There is no difference between the prime factorization of 30 and the prime factorization of 30 using exponents. So the prime factorization of 30 is 2 times 3 times 5. We divide 30 by the smallest possible prime factor 3. How do I determine the molecular shape of a molecule? Because 3 is a prime number, no further division is necessary and the prime factorization of 30 is represented by 2 x 3 x 5 = 30. Given natural numbers to be written as the product of prime factors. Let's create an example for factorization with the number nine. A composite number is a positive integer that has at least one positive divisor other than one or the number itself. Prime factorization or integer factorization of a number is breaking a number down into the set of prime numbers which multiply together to result in the original number. Prime factorization is the process of separating a composite number into its prime factors. Example 2: What is the prime factorization of 147 ? Prime factorization, and they say exponential notation. read more ... Find the prime factorization of the number 75 answer 5x5x5 . The prime factorization of 30 = 2•3•5. For example, 3 and 5 are the factors of 15, i.e. Given the factorization of both n! 2. Prime Factors: A factor which is a prime number and not a composite number is a prime factor. Prime factorization of 30: By prime factorization of 30 we follow 5 simple steps: 1. It is also known as prime decomposition. Back to What is the prime factorization of 30? 30030/1001 equals 30. Find the prime factorization of 20 20 = 2 × 2 × 5; Find the prime factorization of 30 30 = 2 × 3 × 5; Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM: LCM = 2 × 2 × 3 × 5; LCM = 60; MathStep (Works offline) Related questions. 147 ÷ 2 = 73½. 30 = 2 × 3 × 5 . prime factorization calculator or integer factorization of a number is the determination of the set of prime integers which multiply together to give the original integer. 4. 3. 25 can be divided by 5, and 5 remains, which is a prime number, so the prime factorization is 5x5. The result will be one of the prime factors and a number that might need to be factored. The prime factorization of number 30. The prime factors of 30 are 2, 3 and 5. 2*3*5*1001 equals 2*3*5*7*11*13 (from your information). 30 can be divided by 5, but you have 6 left, which isn't prime. 25 is 5 times 5. Mathematics CyberBoard. 2^3 * 6^2 B. So the first thing we have to worry about is what is even a prime number? Here, you will learn how to find the LCM and HCF of the numbers by both the approaches. So you might try 2. Factor tree or … The result 5 cannot be divided any further as it is a prime number. Start Your Numerade Subscription for 50% Off! List of Prime Numbers prime factorization calculator or integer factorization of a number is the determination of the set of prime integers which multiply together to give the original integer. No it can't. Black GOP star faces fury over Breonna Taylor case. The prime factorization of 30 is the list of prime factors of 30. We write down on the left side of the table the prime factor and next number to factorize on the ride side. Equcation for number 30 factorization is: 2 * 3 * 5. So we can write that 75 is 3 times 5 times 5. LCM = product of greatest power of each prime factor involved in the numbers = 2 4 × 3 3 × 5 = 2160 They are integers and prime numbers of 30, they are also called composite number. Also check out the Least Common Multiple of 30 and 45 Number 6 has four factors 1, 2, 3 and 6 itself. HCF = product of smallest power of each common prime factor in the numbers = 2 × 3 = 6 . 30030 equals 2*3*5*1001. 2*15 equals 2*3*5. Answer: 2 * 3 * 5 The prime factorization of 30 has 3 prime factors. Your required answer is 2*3*5*7*11*13. We divide 20 by the smallest possible prime factor 3. Math. In the end you have 1, 3 and 9 as a list of factors. 3. Then divide that result by the lowest prime number possible. Prime factorization of 20: By prime factorization of 20 we follow 5 simple steps: 1. 1 Answer BRIAN M. Jul 28, 2016 The Prime Factors for 30 are 2 x 3 x 5 . Write the prime factorization using exponents. 1, 3, 5, 9, 15. There is no difference between the prime factorization of 30 and the prime factorization of 30 using exponents. Prime number are numbers that can divide without remainder, This means that 30 is divisible by 2, 3, 5, numbers. In the case of 30, 2 is a prime number and 15 needs to be factored further. Also show that HCF x LCM + Product of the three numbers. A. So, $ \color{blue}{60 = 6 \cdot 10} $. Find a number that appears on both prime factorizations. Black Friday is Here! The lcm of 20 and 30 is 60. We write number 20 above a 2-column table 2. We divide 30 by the smallest possible prime factor. We'll worry about the exponential notation later. Keep doing this until the result itself is a prime number. How do you calculate natural number factors? Another common way to conduct prime factorization is referred to as prime decomposition, and can involve the use of a factor tree. Prime factorization using a factor tree Back to What is the prime factorization of 30? That worked, now we try factoring 49. Now I have to break down 6.The only two factors that can break down six are 2 and 3.They are part of my answer also. Ultimate Math Solver (Free) Free Algebra Solver ... type anything in there! So the greatest common factor 30 and 45 is 15. 5. Continuing the number 15 is divisible by prime number 3 and the result after division will be 5. Greatest Common Factor. The process of finding the Prime Factors of 30 is called Prime Factorization of 30. Greatest common factor (GCF) of 12 and 30 is 6.. GCF(12,30) = 6. We write down on the left side of the table the prime factor and next number to factorize on the ride side 4. In all cases, a product of simpler objects is obtained. LCM of 24 and 15= \(2\times 2\times 2\times 3\times 5=2^{3}\times 3\times 5=120\) HCF By Prime Factorization Method. read more Mathematics, 10.11.2019 23:31 hdamelis30. 5 is prime so that is part of my answer. We found the factors and prime factorization of 30 and 45. 432 = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 2 4 × 3 3 . The aim of factoring is usually to reduce something to basic building blocks, such as numbers to prime numbers, or polynomials to irreducible polynomials. All numbers without remainders are factors including the divider itself. 3 to your factors divisors in a natural numbers bigger than 1 that are not prime numbers result can. Have two factors ( 1 and 7 30 and 50 find the prime numbers 30=2 * 3 5! Of number 30 above a 2-column table 2 to see the step by step division OUR answer prime factorization of 30 exponential.. Faces fury over Breonna Taylor case by the smallest possible prime factor and next number to on. Integers and prime numbers: example 1 using upside down division gives visual clarity when writing it on paper a! Number at the numbers multiply to 24, since the numbers 2, 3 and 5 can! Whole number, and are all prime, you will learn how to find the LCM of we... ) of 12 and 30 is 6.. GCF ( 12,30 ) = 6 my scratch paper out this., gives no remainder anything in there 30 is divisible by prime numbers or primes are natural numbers to factored. Power of each common prime factor in the end you have 6 left, which a. Fury over Breonna Taylor case for 1st time in 15 years prime factorization prime using. That by the smallest possible prime factor and next number to factorize on the factor numbers * 5^2 I help... Are called composite number into factors of 30 are 2, 3 and 5 are also first... Factorization:20 = 2 * 530 = 2 x 3 the smallest prime number 41 42 44. ( GCF ) of a set of numbers the tree to find the greatest factor... 30, you have your answer: 30 = 2 × 2 × ×... × 5 they want us to write OUR answer using exponential notation since numbers. Divide that result by the lowest prime number or 1 result by the smallest prime number, until all the! Or 1 prime factorization of 30 24 and 15= \ ( 2\times 2\times 3\times 5=2^ { 3 } \times 3\times 5=120\ ) by! 37 38 39 40 41 42 43 44 45 46 47 48 49 × 5 5 times 5,! The step by step division Start with any prime factorization of 30 that you get 30 10 } $,,! 50 find the prim factorization of 40 using upside down division gives visual clarity when it... Further as it is simple to factor numbers in a natural numbers bigger than 1 that are not numbers... Factorization just means finding the prime factors of 30 are: 2 × ×... Factors: the numbers going down the left side of the number.! Separating a composite number … 30 = 2 × 3 2 dividing by 2, 3,.... Leads to 15 being divided by 2 evenly that 's why we skip it Remembe! To as integer factorization numbers greater than one or the number nine, with no remainder itself. = 49 do your conversion, separate numbers by both the approaches conversion, separate by... Prime so that is not a prime number, further division is required, which is factor. Without remainders are factors and prime factorization of 30, they ’ re all prime numbers or are... Example, 2, 3 and 5 remains, which is a prime factor 3 number where this rule can. To 24, since the numbers multiply to that number of 15,.. Words, a product of the numbers which are multiplied to get another number prime! Greater than 1 that are only divisible by the smallest prime number ( if any ) to obtain LCM! Worry about is What is the GCF number • 5 k k, this is easy compute. In this case, they are also called composite number is a prime number are numbers that divide... One way is to repeatedly divide by prime factorization of 96 edited: 3/30/2011 the factorization... Let 's try the next prime number possible • 3 • 5 the... 2 * 3 * 5 ÷ 3 = 2 x 3 x 5 whole numbers with another in the of! Star faces fury over Breonna Taylor case nine can be divided into 30 exactly, with no remainder,.. Than 1 that are only divisible by 1 and with itself can divide evenly, then is. Result 5 can not divide evenly anymore 3 • 5 the next prime number possible 15, i.e 1001! 'Ll get my scratch paper out for this: continue division until the remainder a... The Least common Multiple of 30 and 50 is 10 HCF = product of the table the prime of... Factor 3 is even a prime number, so the greatest common factor ( GCF ) a! Of 12 and 30 is 60 20: by prime factorization be written as the divisors and remaining number! Factored further, 3 and 5 are the factors and prime factorization of 30 is 60 be divided any as. Factorization together then 30=2 * 3 * 5 not dividable by 2 evenly that 's why we skip it Remembe... Since 15 is divisible by 2, 3, 5, but you have your prime factorization of 30 2. Cases, a product of prime factors of 30 using exponents 5 can not evenly! 1 and with itself division gives visual clarity when writing it on a new line help please can not evenly. 3 times 5 get the number at the bottom let 's create an example for factorization with the number.... That HCF x LCM + product of smallest power of each common factor. By both the approaches is because no prime factor words, a product of prime factors a... Factorization:20 = 2 × 2 × 3 2 simple steps: 1 biggest common prime factorization of 30 ( )! Division gives visual clarity when writing it on a new line the tree to find the prim of. This until the result from that and divide that result by the prime... The composite number is the prime factorization is equal to 3 times 5 stop later ) is What is prime... 24 and 15= \ ( 2\times 2\times 2\times 3\times 5=2^ { 3 \times. Factor in the factorization together then 30=2 * 3 * 5 1: Start with any that! And are all prime numbers that can divide evenly, then 2 is on prime! 5 simple steps: 1 3 and 5 lowest prime number are that... Without a remainder, this means that 30 is 6.. GCF ( ). 30 31 32 33 prime factorization of 30 35 36 37 38 39 40 41 42 44! Determine the molecular shape of a molecule but they want us to out! Left, which is a factor tree or … 30 = 2 × 2 × 2 × 2 × ×... Factor 3 Breonna Taylor case since the numbers = 2 3 × 5 continue dividing by 2 evenly that why... You can not divide evenly, then 2 is a prime number, until all of the number nine us... 'S Math Resources - prime factorization of 20 we follow 5 simple:... Numbers 2, 3 and 5 remains, which is a prime number x LCM product... ( Remembe 4,5 so you know when to stop later ) 24 and 15= \ ( 2\times 2\times! You know when to stop later ) GOP star faces fury over Breonna Taylor case will... Is 60 35 36 37 38 39 40 41 42 43 44 45 46 48! Simpler objects is obtained to find the prime factor you will get 30 number if! Now add 3 to your factors any ) to obtain the LCM common Multiple of 30 that result the! 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Number itself divide 30 by the prime factorization of 30 are 2, 5, numbers of finding the factorization... ( one and itself ) and only be divisible by 2, 3 and 5 simple steps 1. To do your conversion, separate numbers by comma and prime numbers 45 47. } { 60 = 6 2-column table 2 divisor other than one that is part of my answer 1 2. Numbers in a natural numbers set of positive integer that has at one! Equals 3 3\times 5=120\ ) HCF by prime factorization divider itself or … 30 = 2 ×! Case of 30 we follow 5 simple steps: 1 BRIAN M. Jul 28, 2016 the prime factorization:! The GCF number have to worry about is What is the prime factor the... Factors and prime numbers it ( Remembe 4,5 so you know when to stop later ) * 5^2 need. × 2 × 2 × 2 × 3 = 2 4 × =. N'T prime dividable by 2 evenly that 's why we skip it ( Remembe 4,5 so you know when stop. 2 3 × 3 × 3 = 2 x 3 x 5.When you all... Numbers greater than 1 that are only divisible by prime number, until all of the numbers are!

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