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# What is the greatest common factor of 32 and 36?

Mar 7, 2018

GCF = 4

#### Explanation:

Greatest Common Factor is :
4
Calculate Greatest Common Factor for :
32, 36

Factorize of the above numbers :
$32 = {2}^{5} = {2}^{2} \cdot {2}^{3}$
$36 = {2}^{2} \cdot {3}^{2}$

Hope I helped, Good day!

Mar 7, 2018

$G C F \left(32 , 36\right) = \textcolor{red}{4}$

#### Explanation:

Since
$\textcolor{w h i t e}{\text{XXX}} 32 = \textcolor{red}{4} \times \textcolor{g r e e n}{8}$
and
$\textcolor{w h i t e}{\text{XXX}} 36 = \textcolor{red}{4} \times \textcolor{m a \ge n t a}{9}$

and since $\textcolor{g r e e n}{8}$ and $\textcolor{m a \ge n t a}{9}$ obviously have no common factors (other than $1$)

$\textcolor{red}{4}$ must be the greatest common factor of $32$ and $36$