What is the greatest common factor for 12 and 15?

Question

Nova Allen · Accepted Answer

#3#

The GCF of #12# and #15# is #3#.

#color(white)()# One way to find this is to break down these two numbers into their prime factorisations:

#12 = 2 xx 2 xx 3#

#15 = 3 xx 5#

We see that the only common factor (greater than #1#) is #3#, so that is the greatest common factor. If the two numbers had more than one prime factor in common, you would multiply them together to find the GCF.

#color(white)()# Another method, which does not require us to factor both of the numbers first goes as follows:

#color(white)()# Divide the larger number by the smaller number to give a quotient and remainder.

If the remainder is zero then the smaller number is the GCF.

Otherwise repeat with the smaller number and the remainder.

#color(white)()# In our example:

#15 / 12 = 1# with remainder #3#

#12 / 3 = 4# with remainder #0#

So the GCF is #3#.

Riley Anderson · Answer

undefined The greatest common factor (GCF) for 12 and 15 is 3.