# What is the greatest common factor of 16 and 40?

May 9, 2018

8

#### Explanation:

16 divided by 8 is 2.
40 divided by 8 is 5.
Neither of these can be reduced by any more common numbers, so therefore, 8 is your greatest common factor.

May 9, 2018

The GCF of 16 and 40 is 8.

#### Explanation:

Make a factor tree of each number:

1 - 16
2 - 8
4 - 4
8 -2
16 - 1

1 - 40
2 - 20
4 - 10
5 - 8
8 - 5
10 - 4
20 - 2
40 - 1

8

#### Explanation:

When doing GCF (Greatest Common Factor) questions, I like to do a prime factorization first:

$16 = 2 \times 2 \times 2 \times 2$
$40 = 2 \times 2 \times 2 \times 5$

For GCF, we want all the primes that are common to both our numbers. See that there are three 2's in both 16 and 40. We don't use the fourth 2 since only the 16 has that and we don't use the 5 because only the 40 has that. Therefore, the GCF is 8:

$8 \times 5 = 40$
$8 \times 2 = 16$