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All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this.
Example: 210

210 Divide by two.
105,2 Divide by three.
35,3,2 Divide by five.
7,5,3,2 Stop. All the factors are prime.

2 x 3 x 5 x 7 = 210
That's the prime factorization of 210.

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What does the prime factorization of a number mean?

You can think of a factor as a number that divides another number with no remainder. For example, 3 is a factor of 6 since 3 goes into 6 two times with no remainder. Now if the factor is prime, then it is a prime factor. So in the example above, 3 is a prime factor. This is because the factor itself has only two factors, 1 and itself. 6 goes into itself also, but since 6 is not prime, it is not a prime factor. Now that you understand it, here is a more precise definition. A prime factor is a factor that is a prime number. In other words, one of the prime numbers that, when multiplied, give the original number.


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The GCF of 14, 31, 39, and 56 is 1. One way to solve the problem is to notice that 31 is prime, and can't possibly be a factor of 14, which is smaller.If you prefer, you can write the prime factorization of each number in the set and find the GCF:The prime factorization of 14 is 2*7The prime factorization of 31 is 31 (1*31)The prime factorization of 39 is 3*39The prime factorization of 56 is 2*2*2*7So the GCF is 1.


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No prime power exists since there are no duplicate prime numbers in the prime factorization.

Related Questions

What diagram is used to write the prime factorization of a number?

a factor tree


How do you write a factor tree for a prime number?

The purpose of a factor tree is to notate the process of finding the prime factorization. If a number is already prime, a factor tree is not necessary.


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