# 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.

Then teach the underlying concepts
Don't copy without citing sources
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#### Explanation

Explain in detail...

#### Explanation:

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