Question

Find the Hcf of 300,360 and 240 by prime factorization method​

Answer 1

$\textbf{Given:}$

$\text{Numbers: 300, 360 and 240}$

$\textbf{To find:}$

$\text{HCF of the given numbers}$

$\textbf{Solution:}$

$\begin{array}{r|l}2&300\\\cline{2-2}2&150\\\cline{2-2}3&75\\\cline{2-2}5&25\\\cline{2-2}5&5\\\cline{2-2}&1\\\cline{2-2}\end{array}$

$\begin{array}{r|l}2&360\\\cline{2-2}2&180\\\cline{2-2}2&90\\\cline{2-2}3&45\\\cline{2-2}3&15\\\cline{2-2}5&5\\\cline{2-2}&1\\\cline{2-2}\end{array}$

$\begin{array}{r|l}2&240\\\cline{2-2}2&120\\\cline{2-2}2&60\\\cline{2-2}2&30\\\cline{2-2}3&15\\\cline{2-2}5&5\\\cline{2-2}&1\\\cline{2-2}\end{array}$

$\text{We get}$

$300=\boxed{2{\times}2}{\times}\boxed{3}{\times}\boxed{5}{\times}5$

$360=\boxed{2{\times}2}{\times}2{\times}\boxed{3}{\times}3{\times}\boxed{5}$

$240=\boxed{2{\times}2}{\times}2{\times}2{\times}\boxed{3}{\times}\boxed{5}$

$H.C.F=2{\times}2{\times}3{\times}5$

$\implies\bf\,H.C.F=60$

$\therefore\textbf{H.C.F of 300, 360 and 240 is 60}$

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