Question

Find the greatest common factor of the following monomials: 20a3 and 8a2

Answer 1

GCF of given monomials are $4a^2$

Solution:

Given that we have to find the greatest common factor

Given monomials are:

$20a^3 \text{ and } 8a^2$

When we find all the factors of two or more numbers, and some factors are the same, then the largest of those common factors is the Greatest Common Factor

Let us first find the GCF of 20 and 8 and then find GCF of variables and then multiply them together

GCF of 20 and 8:

The factors of 8 are: 1, 2, 4, 8

The factors of 20 are: 1, 2, 4, 5, 10, 20

Then the greatest common factor is 4

$GCF\ of\ a^3 \text{ and } a^2\\\\a^3 = a^2 \times a\\\\a^2 = a^2$

Thus GCF is $a^2$

Therefore GCF of monomials are:

$\text{GCF of } 20a^3 \text{ and } 8a^2 = 4 \times a^2 = 4a^2$

Thus GCF of given monomials are $4a^2$