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## what is the GCF that 30 and also 75?

Method I: List all of the determinants of the 2 numbers and also find the largest number the lists have actually in common.

30:1,2,3,5,6,10,15,3075:1,3,5,15,25,75

Thus the GCF is 15.

an approach II: A much more general method, and one that works...

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## what is the GCF the 30 and 75?

Method I: List all of the components of the 2 numbers and find the largest number the lists have actually in common.

30:1,2,3,5,6,10,15,3075:1,3,5,15,25,75

Thus the GCF is 15.

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

First we compose each number together a product of prime factors.

30=2*3*575=3*5*5

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

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