Method 1: Use a list of factors to find the GCF
This method for finding the GCF is quicker when you’re dealing with smaller numbers. To find the GCF of a set of numbers, list all the factors of each number. The greatest factor appearing on every list is the GCF. For example, to find the GCF of 6 and 15, first list all the factors of each number.Factors of 6: 1, 2, 3, 6
Factors of 15: 1, 3, 5, 15
Because 3 is the greatest factor that appears on both lists, 3 is the GCF of 6 and 15.
As another example, suppose you want to find the GCF of 9, 20, and 25. Start by listing the factors of each:
Factors of 9: 1, 3, 9
Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 25: 1, 5, 25
In this case, the only factor that appears on all three lists is 1, so 1 is the GCF of 9, 20, and 25.
Method 2: Use prime factorization to find the GCF
You can use prime factorization to find the GCF of a set of numbers. This often works better for large numbers, where generating lists of all factors can be time-consuming.Here’s how to find the GCF of a set of numbers using prime factorization:
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List the prime factors of each number.
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Circle every common prime factor — that is, every prime factor that’s a factor of every number in the set.
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Multiply all the circled numbers.
The result is the GCF.
As you can see, the numbers 2 and 7 are common factors of all three numbers. Multiply these circled numbers together:
2 · 7 = 14
Thus, the GCF of 28, 42, and 70 is 14.
Knowing how to find the GCF of a set of numbers is important when you begin reducing fractions to lowest terms.