How do you find the GCF of 9 and 15 and 24?

GCF = 3

Explanation:

A factor is a number that when multiplied by another number, gives us the number in question. So for instance 3 is a factor of 9 because $3 \times 3 = 9$.

The GCF is the highest number that is a factor of all three of our "test subject numbers".

So let's do a prime factorization of all three to start things out and I'll colour the different prime values in different colours:

$9 = \textcolor{red}{3} \times \textcolor{red}{3}$
$15 = \textcolor{red}{3} \times \textcolor{b l u e}{5}$
$24 = \textcolor{g r e e n}{2} \times \textcolor{g r e e n}{2} \times \textcolor{g r e e n}{2} \times \textcolor{red}{3}$

Ok, now let's find what is common.

2

There are 2s in 24 but not in 9 or 15, so there are no 2s in our GCF.

3

There is one 3 in 24 and in 15 and two in 9 - so one 3 is common to all three numbers.

5

There is a 5 in 15 but not in 9 or 24, so the GCF doesn't have a 5.

And there are no more prime numbers.

This means our GCF = 3.

$3 \times 3 = 9$
$3 \times 5 = 15$
$3 \times 8 = 24$