Question

find the HCF of 140 and 504 pls give the explanation

Answer 1

Solution:

1st expression=140

                       =2*2*5*7  

2nd expression=504

                        =2*2*2*3*3*7

HCF =2*2*7=28

Here, all the commons are taken.

And we got answer as 28.

Answer 2

$\textbf{\large{\underline{Answer :-}}}$

The HCF of 140 and 504 is 28

$\textbf{\large{\underline{Explaination :-}}}$

$\textbf{Prime factorization of 140}$

$\begin{array}{r|l}2 & 140 \\\cline{1-2} 2& 70\\\cline{1-2} 5 & 35\\ \cline{1-2} 7 & 7 \\\cline{1-2} & 1\end{array}$

$\textbf{Prime factorization of 504}$

$\begin{array}{r|l}2 & 504 \\\cline{1-2} 2 & 252\\\cline{1-2} 2 & 126\\ \cline{1-2} 3 & 63\\\cline{1-2} 3 & 21\\\cline{1-2}7&7\\\cline{1-2}&1\end{array}$

$\tt{\rightarrow 140 = 2\times 2\times 5 \times7}$

$\tt{\rightarrow 504 = 2 \times 2 \times 2\times 3 \times 3 \times7}$

Make pair of common factors and take only one from them.

Common pairs =

$\tt{\rightarrow 2 \times 2}$

$\tt{\rightarrow 2 \times 2}$

$\tt{\rightarrow 7 \times 7}$

$\tt{\Rightarrow HCF = 2 \times 2 \times 7}$

$\tt{\Rightarrow 4 \times 7}$

$\tt{\Rightarrow 28}$

$\therefore$The HCF of of 140 and 504 is 28