Question

Find H.C.F of 144 ,180, 96.​

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{144, 180, 96}$

$\underline{\textbf{To find:}}$

$\textsf{H.C.F of the given numbers}$

$\underline{\textbf{Solution:}}$

$\textsf{We find the HCF by prime factorization method}$

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

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

$\mathsf{96=2^5{\times}3}$

$\textsf{Now we find out the common factors}$

$\mathsf{144=\boxed{2}{\times}\boxed{2}{\times}2{\times}2{\times}\boxed{3}{\times}3}$

$\mathsf{180=\boxed{2}{\times}\boxed{2}{\times}\boxed{3}{\times}3{\times}5}$

$\mathsf{96=\boxed{2}{\times}\boxed{2}{\times}2{\times}2{\times}2{\times}\boxed{3}}$

$\mathsf{H.C.F=2{\times}2{\times}3}$

$\implies\boxed{\boxed{\mathsf{H.C.F=12}}}$

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