Greatest Common Factor

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

Example 1

Example

Solution

Find the prime factorization of 18 and 60.

18 = 2⋅32
60 = 22⋅3⋅5

Write 18 = 2⋅32.
Write 60 = 22⋅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 22.
So write, the less exponent power, 2.

18 has 32.
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.

Example 2

Example

Solution

Write the prime factorizations of the monomials.

Write 6a3c = 2⋅3⋅a3⋅c.
Write 2a2bc2 = 2⋅a2⋅b⋅c2 in the next line.

Compare the same base powers
and write the less exponent power
in the GCF.

6a3c has 2.
2a2bc2 also has 2.
So write 2.

6a3c has 3.
2a2bc2 doesn't have 3.
So don't write 3.

6a3c has a3.
2a2bc2 has a2.
So write, the less exponent power, a2.

6a3c doesn't have b.
2a2bc2 has b.
So don't write b.

6a3c has c.
2a2bc2 has c2.
So write, the less exponent power, c.

So the greatest common factor of 6a3c and 2a2bc2 is
2a2c.