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

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The Lonely Donut
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Feb 12, 2017

#### Answer:

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.

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