Question
Find the $HCF$ of the numbers in the following using the prime factorization method:$144, 252, 630$
✓
Answer
The given numbers are $144, 252$ and $630$.We have:
$\begin{array}{c|c}2&144\\\hline2&72\\\hline2&36\\\hline2&18\\\hline3&9\\\hline3&3\\\hline&1\end{array}$
$\begin{array}{c|c}2&252\\\hline2&126\\\hline3&63\\\hline3&21\\\hline7&7\\\hline&1\end{array}$
$\begin{array}{c|c}2&630\\\hline3&315\\\hline3&105\\\hline5&35\\\hline7&7\\\hline&1\end{array}$
Now, $144=2\times2\times2\times2\times3\times3$
$252=2\times2\times3\times3\times7$
$630=2\times3\times3\times5\times7$
$\therefore HCF =2\times3\times3=18$
$\begin{array}{c|c}2&144\\\hline2&72\\\hline2&36\\\hline2&18\\\hline3&9\\\hline3&3\\\hline&1\end{array}$
$\begin{array}{c|c}2&252\\\hline2&126\\\hline3&63\\\hline3&21\\\hline7&7\\\hline&1\end{array}$
$\begin{array}{c|c}2&630\\\hline3&315\\\hline3&105\\\hline5&35\\\hline7&7\\\hline&1\end{array}$
Now, $144=2\times2\times2\times2\times3\times3$
$252=2\times2\times3\times3\times7$
$630=2\times3\times3\times5\times7$
$\therefore HCF =2\times3\times3=18$
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