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

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Answer 1 · 2017-01-10T04:24:44

GCF = 3

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 $3xx3=9$ .

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:

$9=color(red)(3)xxcolor(red)(3)$
$15=color(red)(3)xxcolor(blue)(5)$
$24=color(green)(2)xxcolor(green)(2)xxcolor(green)(2)xxcolor(red)(3)$

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.

$3xx3=9$
$3xx5=15$
$3xx8=24$