# Greatest Common Factor

How to find the greatest common factor (GCF) of the given numbers and monomials: 2 examples and their solutions.

## ExampleGCF of 18 and 30

Find the prime factorization of 18 and 60.

18 = 2⋅3^{2}

60 = 2^{2}⋅3⋅5

Write 18 = 2⋅3^{2}.

Write 60 = 2^{2}⋅3⋅5 in the next line.

Then find the GCF:

the greatest common factor.

Compare the same base powers

and write the less exponent power

in the GCF.

18 has 2.

60 has 2^{2}.

So write, the less exponent power, 2.

18 has 3^{2}.

60 has 3.

So write, the less exponent power, 3.

18 doesn't have 5.

60 has 5.

So don't write 5.

So the GCF of 18 and 60 is 2⋅3.

2⋅3 = 6

So 6 is the greatest common factor of 18 and 60.

## ExampleGCF of 6a^{3}c and 2a^{2}bc^{2}

Write the prime factorizations of the monomials.

Write 6a^{3}c = 2⋅3⋅a^{3}⋅c.

Write 2a^{2}bc^{2} = 2⋅a^{2}⋅b⋅c^{2} in the next line.

Compare the same base powers

and write the less exponent power

in the GCF.

6a^{3}c has 2.

2a^{2}bc^{2} also has 2.

So write 2.

6a^{3}c has 3.

2a^{2}bc^{2} doesn't have 3.

So don't write 3.

6a^{3}c has a^{3}.

2a^{2}bc^{2} has a^{2}.

So write, the less exponent power, a^{2}.

6a^{3}c doesn't have b.

2a^{2}bc^{2} has b.

So don't write b.

6a^{3}c has c.

2a^{2}bc^{2} has c^{2}.

So write, the less exponent power, c.

So the greatest common factor of 6a^{3}c and 2a^{2}bc^{2} is

2a^{2}c.