Question

What is the greatest common factor of 6, 12, and 25?

Answer 1

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`

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 = 3 * 2 * 2 * 1`

`12 = 3 * 2^2 * 1`

Finally, 25:

`25 = 5 * 5 * 1`

`25 = 5^2 * 1`

The only factors that are written throughout our prime factorization are

`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.