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# How do you find the GCF of 20 and 28?

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#### Explanation

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#### Explanation:

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Jan 12, 2017

The GCF of $20$ and $28$ is $4$

#### Explanation:

Here are a few methods (in no particular order). Each method has its advantages and disadvantages in different kinds of examples.

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Method 1 - Subtraction

Given two positive whole numbers, you can find their GCF as follows:

• If the numbers are the same as one another then that is their GCF.

• Otherwise, replace the larger number with the result of subtracting the smaller number from it and repeat.

In our example:

• Given: $\textcolor{b l u e}{20 , 28}$

• Replace $28$ with $28 - 20 = 8$ to get: $\textcolor{b l u e}{20 , 8}$

• Replace $20$ with $20 - 8 = 12$ to get: $\textcolor{b l u e}{12 , 8}$

• Replace $12$ with $12 - 8 = 4$ to get: $\textcolor{b l u e}{4 , 8}$

• Replace $8$ with $8 - 4 = 4$ to get: $\textcolor{b l u e}{4 , 4}$

• So the GCF is $\textcolor{b l u e}{4}$

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Method 2 - Division

Given two positive whole numbers, you can find their GCF as follows:

• Divide the larger number by the smaller to give a quotient and remainder.

• If the remainder is $0$ then the smaller number is the GCF.

• Otherwise, repeat with the smaller number and the remainder.

So in our example:

$\frac{28}{20} = 1 \text{ }$ with remainder $8$

$\frac{20}{8} = 2 \text{ }$ with remainder $4$

$\frac{8}{4} = 2 \text{ }$ with remainder $0$

So the GCF is $4$

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Factoring

To find the GCF of two positive whole numbers, find their prime factorisations and multiply the common factors together.

In our example:

$20 = 2 \cdot 2 \cdot 5$

$28 = 2 \cdot 2 \cdot 7$

So the GCF is:

$2 \cdot 2 = 4$

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