Question

7
Find the GCF of the pair of monomials.
32a,48a

Answer 1

The greatest common factor (GCF) of these two monomials is
`16\, a`.

Explanation:

Rewrite
`32\, a` and
`48\, a` as the products of the variable
`a` and and prime number factors:

• 
  `32\, a = 2 * 2 * 2 * 2 * 2 * a = 2^(5)* a` (where
  `2` is a prime factor.)
• 
  `48\, a = 2 * 2* 2 * 2 * 3* a = 2^(4)* 3* a` (where
  `2` and
  `3` are both prime factors.)

Write an expression for the GCF of these two monomials in terms of these factors (
`2`'s,
`3`, and
`a`.) Try to include as many of each factor as possible, as long as the resulting product is present in both monomials.

For example, there are five factor
`2`'s in the first monomial but only four in the second monomial. Therefore, include the factor
`2\!` in the GCF for only four times.

The factor
`a` appeared once in both monomials. Hence, include
`a\!` for one in the expression for the GCF.

On the other hand, the factor
`3` is found in the second monomial but not in the first. Therefore, this factor should not be included in the expression for the GCF.

Therefore, the expression for the GCF would be:

`2 * 2* 2* 2 * a = 16\, a`.