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It's often useful in solving math problems to be able to find the largest factor that divides two numbers. We call this the greatest common factor, or GCF. Let's find the GCF of 30 and 45. First we find the prime factors of each number, using prime factorization.

30 = 2 × 3 × 5
45 = 3 × 3 × 5

Next, identify those prime factors that both numbers have in common, and multiply them. Here, both 3 and 5 are common factors. The GCF is 3 times 5, or 15.

3 × 5 = 15 <— GCF

EXAMPLES

Find the GCF of these pairs of numbers.

14, 49
Solution: List the prime factors of each.
14: 2 × 7
49: 7 × 7
7 is the only common factor; therefore, 7 is the GCF.

15, 75
Solution: List the prime factors of each.
15: 3 × 5
75: 3 × 5 × 5
3 and 5 are common; therefore, 3 × 5 = 15 is the GCF.

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