If H.C.F. of $144$ and $180$ is expressed in the form $13m-16$. find the value of m.

Given: H.C.F. of $144$ and $180$ is expressed in the form $13m-16$.

To do: To find the value of $m$.

Solution: 

$144 = 2 ^ {4} \times 3 ^ {2}$

$180= 2 ^ {2} \times 5 \times 3 ^ {2}$

$\therefore H.C.F ( 180,\ 144) = 2 ^ {2} \times 3 ^ {2} = 4 \times 9 = 36$

$\because$ H.C.F. of $144$ and $180$ is expressed in the form $13m-16$.

$\therefore 13m - 3 = 36$

$\Rightarrow 13m = 39$

$\Rightarrow m = 3$

$\therefore m = 3$

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Updated on: 10-Oct-2022

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