# How do you find the greatest common factor of 88, 55?

Oct 28, 2016

$\therefore G C F \left(88 , 55\right) = 11$

#### Explanation:

repeated use of Euclidean Algorithm

$\textcolor{red}{88} = 1 \times \textcolor{b l u e}{55} + \textcolor{g r e e n}{33}$

$\textcolor{b l u e}{55} = 1 \times \textcolor{g r e e n}{33} + \textcolor{}{22}$

$\textcolor{g r e e n}{33} = 1 \times 22 + \textcolor{m a \ge n t a}{11}$

$22 = 2 \times \textcolor{m a \ge n t a}{11} + 0$

last non zero remainder =$11$

$\therefore G C F \left(88 , 55\right) = 11$

Oct 28, 2016

GCF = 11

#### Explanation:

This method uses only $\textcolor{b l u e}{\text{subtraction}}$ to find the greatest common factor ( GCF ).

•" subtract smaller number from larger number"

•" Repeat this until a common value is obtained"

•" The common value is the GCF"
$\textcolor{b l u e}{\text{-----------------------------------------}}$

•88" and " 55larrcolor(red)"starting numbers"

$88 - 55 = 33 \leftarrow \text{ larger subtract smaller}$

•55" and "33larrcolor(red)" numbers after subtraction"

$55 - 33 = 22 \leftarrow \text{ larger subtract smaller}$

•33" and " 22larrcolor(red)" numbers after subtraction"

$33 - 22 = 11 \leftarrow \text{ larger subtract smaller}$

•22" and " 11larrcolor(red)" numbers after subtraction"

$22 - 11 = 11 \leftarrow \text{ larger subtract smaller}$

•11" and " 11larrcolor(magenta)" common value reached"

$\Rightarrow \text{ GCF of 88 and 55 } = 11$