The greatest common factor, or GCF, of two numbers is the largest value that divides into each of the numbers. Let’s take, for instance, 18 and 30.

You can find the GCF of two numbers by finding the prime factorization of your numbers, and then finding what they have in common.

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The transcript is for your convenience

So, the prime factorization of 18 – 18 is even, so it’s divisible by 2, so 2*9 would be 18, 9 is not prime nos., so we need to break 9 down, and the factors of 9 are 3*3.

So, the prime factorization of 18 would be 2*3*3. 3*3 is 9, times 2 is 18. I always like to check after I factor to make sure I’ve got it.

The prime factorization of 30 – 30 is divisible by 2 also since it’s even, so 2*15 would be 30, but 15 is not prime, so we have to break it down into its prime factors, and 15’s prime factors are 3*5.

So, the prime factorization of 30 is 2*3*5. 2*3 is 6, and 6*5 is 30.

Now, again, to find the GCF, we’re going to look for what they have in common. 18 and 30 have 2 and 3 in common as prime factors.

So, we take those factors they have in common and multiply them. 2*3 is 6, so the GCF of 18 and 30 is 6. 6 is the largest factor that these numbers have in common.

When we find all the factors of two or more numbers, and some factors are the same (“common”), then the largest of those common factors is the Greatest Common Factor.

Abbreviated “GCF”. Also called “Highest Common Factor