What is the greatest common factor of 6, 12, and 25?
1 Answer
Feb 12, 2017
The GCF is 1.
Explanation:
First, we have to break down each number to its prime factors.
Let's take the number 6 first:
6 = 2 * 3 * 1 6=2⋅3⋅1
Although multiplying by 1 is not necessary, sometimes it helps visualize and understand (like in this case) that the GCF is 1.
Now 12:
12 = 6 * 2 * 1 12=6⋅2⋅1
12 = 3 * 2 * 2 * 1 12=3⋅2⋅2⋅1
12 = 3 * 2^2 * 1 12=3⋅22⋅1
Finally, 25:
25 = 5 * 5 * 1 25=5⋅5⋅1
25 = 5^2 * 1 25=52⋅1
The only factors that are written throughout our prime factorization are
1, 2, 3, 5 1,2,3,5
However, not all of the numbers share all of the factors. The only (and the greatest) factor that all three numbers share is the number 1. So the answer is 1.
