Question

How do you find the GCF of 20 and 28?

Answer 1

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: `color(blue)(20, 28)`

• Replace `28` with `28-20 = 8` to get: `color(blue)(20, 8)`

• Replace `20` with `20-8 = 12` to get: `color(blue)(12, 8)`

• Replace `12` with `12-8=4` to get: `color(blue)(4, 8)`

• Replace `8` with `8-4=4` to get: `color(blue)(4, 4)`

• So the GCF is `color(blue)(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:

`28/20 = 1" "` with remainder `8`

`20/8 = 2" "` with remainder `4`

`8/4 = 2" "` 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*2*5`

`28=2*2*7`

So the GCF is:

`2*2 = 4`