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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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