# What is the GCF of 36 and 60?

Mar 31, 2016

Greatest Common Factor is $12$.

#### Explanation:

Factors of $36$ are $\left\{1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 36\right\}$.

Factors of $60$ are $\left\{1 , 2 , 3 , 4 , 5 , 6 , 10 , 12 , 15 , 20 , 30 , 60\right\}$.

Common factors are }1,2,3,4,6,12}.

Hence Greatest Common Factor is $12$.

Aug 24, 2016

$H C F = 2 \times 2 \times 3 = 12$

#### Explanation:

A method of finding GCF and LCM - especially of several numbers if they are larger than usual - is to write the numbers as the product of the prime factors.

In this way we can immediately see which factors are common:

$\textcolor{w h i t e}{\times \times \times} 36 = \textcolor{red}{2 \times 2 \times 3} \times 3$
$\textcolor{w h i t e}{\times \times \times} 60 = \textcolor{red}{2 \times 2 \times 3} \textcolor{w h i t e}{\times x} \times 5$

$G C F = \textcolor{w h i t e}{\times} = \textcolor{red}{2 \times 2 \times 3} \textcolor{w h i t e}{\times \times x} = 12$

$L C M = \textcolor{w h i t e}{\times} = 2 \times 2 \times 3 \times 3 \times 5 \textcolor{w h i t e}{\times \times x} = 180$

If you have any number written as the product of its prime factors, then you know everything there is to know about that number.