Question

How do you find the GCF of 98 and 28?

Answer 1

`14`

Explanation:

Here are a couple of methods:

Method 1 - Division and remainder

To find the GCF of two numbers proceed as follows:

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

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

• Otherwise repeat with the smaller number and remainder.

In our example, we find:

`98 / 28 = 3" "` with remainder `14`

`28 / 14 = 2" "` with remainder `0`

So the GCF of `98` and `28` is `14`

Method 2 - Prime factorisation

Factorise `98` and `28` down to their prime factors, and identify the factors which are common - including multiplicity.

`color(white)(00000)98color(white)(0000000000)28`
`color(white)(0000)"/"color(white)(00)"\"color(white)(00000000)"/"color(white)(00)"\"`
`color(white)(000)2color(white)(000)49color(white)(000000)2color(white)(000)14`
`color(white)(000000)"/"color(white)(00)"\"color(white)(00000000)"/"color(white)(00)"\"`
`color(white)(00000)7color(white)(0000)7color(white)(000000)2color(white)(0000)7`

So:

`98 = 2 xx 7 xx 7`

`28 = 2 xx 2 xx 7`

The common factors in the common multiplicities give us the GCF when multiplied:

`"GCF" = 2 xx 7 = 14`