Question

find the HCF of 252525 and 363636​

Answer 1

$\textbf{To find:}$

$\text{HCF of 252525 and 363636}$

$\textbf{Solution:}$

$\text{We find the H.C.F by prime factorization method}$

$\begin{array}{r|l}3&252525\\\cline{2-2}5&8475\\\cline{2-2}5&16835\\\cline{2-2}7&3367\\\cline{2-2}13&481\\\cline{2-2}37&37\\\cline{2-2}&1\\\cline{2-2}\end{array}$

$\begin{array}{r|l}2&363636\\\cline{2-2}2&181818\\\cline{2-2}3&90909\\\cline{2-2}3&30303\\\cline{2-2}3&10101\\\cline{2-2}7&3367\\\cline{2-2}13&481\\\cline{2-2}37&37\\\cline{2-2}&1\\\cline{2-2}\end{array}$

$\text{From the above factorization, we get}$

$252525=2^2{\times}3^2{\times}\boxed{3{\times}7{\times}13{\times}37}$

$363636=\boxed{3}{\times}5^2{\times}\boxed{7{\times}13{\times}17}$

$\textbf{H.C.F}=3{\times}7{\times}13{\times}37$

$\implies\textbf{H.C.F=10101}$

$\therefore\textbf{The H.C.F of 252525 and 363636 is 10101}$

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Answer 2

Therefore the HCF = 10101