# How do you find the GCF of 98 and 28?

Nov 8, 2016

$14$

#### 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:

$\frac{98}{28} = 3 \text{ }$ with remainder $14$

$\frac{28}{14} = 2 \text{ }$ 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.

$\textcolor{w h i t e}{00000} 98 \textcolor{w h i t e}{0000000000} 28$
$\textcolor{w h i t e}{0000} \text{/"color(white)(00)"\"color(white)(00000000)"/"color(white)(00)"\}$
$\textcolor{w h i t e}{000} 2 \textcolor{w h i t e}{000} 49 \textcolor{w h i t e}{000000} 2 \textcolor{w h i t e}{000} 14$
$\textcolor{w h i t e}{000000} \text{/"color(white)(00)"\"color(white)(00000000)"/"color(white)(00)"\}$
$\textcolor{w h i t e}{00000} 7 \textcolor{w h i t e}{0000} 7 \textcolor{w h i t e}{000000} 2 \textcolor{w h i t e}{0000} 7$

So:

$98 = 2 \times 7 \times 7$

$28 = 2 \times 2 \times 7$

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

$\text{GCF} = 2 \times 7 = 14$