How do I find the greatest common factor of 12 and 32

Don't just give me the answer. I want to learn how you came upon that conclusion. Please and thank you.

Both answers above are correct. But, there is another way. It is by using the Euclidean algorithm. To do this, we take the larger number and write it as the product of the smaller one plus a remainder. Then in the next step, we take the smaller number from above and use the remainder we found to write it as the product of the first remainder, a quotient and a new remainder. We keep doing this until the remainder is 0. Then the greatest common divisor will be the remainder of the line right above this final line with remainder zero. Let's try it:

32 = 12(2) + 8
12 = 8(1) + 4
8 = 4(2) + 0.

So, gcd(12, 32) = 4, by the Euclidean Algorithm.

Factor each number into its prime factorization.

12 = 2 x 2 x 3
32 = 2 x 2 x 2 x 2 x 2

So, the greatest common factor is 2 x 2 = 4

Use the prime factors.

12 = 2 * 2 * 3

32 = 2 * 2 * 2 * 2 * 2

So they have 2 of the 2s in common, and 2 * 2 = 4

list the factors of each and then select those that are common to both

32 = 2*2*2*2*2
12 = 2*2*3

So 2*2