Question

find hcf of 144, 96, 54 by prime factorisation

Answer 1

$\textbf{Given numbers are 144, 96, 54}$

$\textbf{To find:} HCF$

$\begin{array}{r|l}2&144\\\cline{2-2}2&72\\\cline{2-2}2&36\\\cline{2-2}2&18\\\cline{2-2}3&9\\\cline{2-2}3&3\\\cline{2-2}&1\\\cline{2-2}\end{array}$

$\begin{array}{r|l}2&96\\\cline{2-2}2&48\\\cline{2-2}2&24\\\cline{2-2}2&12\\\cline{2-2}2&6\\\cline{2-2}3&3\\\cline{2-2}&1\\\cline{2-2}\end{array}$

$\begin{array}{r|l}2&54\\\cline{2-2}3&27\\\cline{2-2}3&9\\\cline{2-2}3&3\\\cline{2-2}&1\\\cline{2-2}\end{array}$

$\text{Now,}$

$\bf\,144=\boxed{2}{\times}2{\times}2{\times}2{\times}\boxed{3}{\times}3$

$\bf\,96=\boxed{2}{\times}2{\times}2{\times}2{\times}2{\times}\boxed{3}$

$\bf\,54=\boxed{2}{\times}\boxed{3}{\times}3{\times}3$

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

$\bf\,H.C.F=6$

$\therefore\textbf{HCF of 144, 96 and 54 is 6}$

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Answer 2

Given:

144, 96 and 54

To find, the HCF of  144, 96, 54 by prime factorisation.

Solution:

144 = 2 × 2 × 2 × 2 × 3 × 3

96 = 2 × 2 × 2 × 2 × 2 × 3 and

54 = 2 × 3 × 3 × 3

The common prime factor of  144, 96 and 54 = 2 × 3

∴ The HCF of  144, 96, 54 by prime factorisation = 6

Thus, the HCF of  144, 96, 54 by prime factorisation is equal to 6.