how do you find the greatest common factor of 2 numbers?

Answer 1

Here are two ways to do it:

1. Take the prime factorization of your two numbers. Multiply together the smallest exponents you have on each term. For example, to find the greatest common factor of 24 and 60:

24 = 2^3 x 3
60 = 2^2 x 3 x 5

The smallest exponent on 2 is 2; the smallest exponent on 3 is 1; the smallest exponent on 5 is 0 (since it doesn't appear at all in 24). So we have that the greatest common factor is

2^2 x 3 = 12.

2. Use the Euclidean Algorithm. This works as follows:

(i) Divide the bigger number by the smaller.
(ii) Replace the bigger number with the REMAINDER you got in step 1.
(iii) If one of the numbers is zero, stop; the GCF is your other number.
(iv) Otherwise, go back to step (i) with the two new numbers you have.

Example with 24 and 60:

First, 60 divided by 24 leaves a remainder of 12. So our new two numbers are 12 and 24. Neither is zero, so we do the same thing again.

Next, 24 divided by 12 leaves a remainder of 0. So our new two numbers are 0 and 12. One of them is zero, so our GCF is the other number, 12.

(You might have to repeat this process many times for some pairs of numbers).

I hope that this is of some help to you.

Answer 2

i concurr