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

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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:

$6 = 2 \cdot 3 \cdot 1$

Although multiplying by 1 is not necessary, sometimes it helps visualize and understand (like in this case) that the GCF is 1.

Now 12:

$12 = 6 \cdot 2 \cdot 1$

$12 = 3 \cdot 2 \cdot 2 \cdot 1$

$12 = 3 \cdot {2}^{2} \cdot 1$

Finally, 25:

$25 = 5 \cdot 5 \cdot 1$

$25 = {5}^{2} \cdot 1$

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.

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