## what is the GCF of 30 and 75?

Method I: List all of the factors of the two numbers and find the largest number the lists have in common.

30:1,2,3,5,6,10,**15**,30

75:1,3,5,**15**,25,75

**Thus the GCF is 15.**

Method II: A more general method, and one that works better with many factors or problems involving variables.

First we write each number as a product of prime factors.

30=2*3*5

75=3*5*5

We then circle any number that appears in both lists -- in this case we have a 3 and a 5 in both lists. The GCF will be the product of these common factors, or **GCF=3*5=15.**

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