Question

Find the greatest number which can divide $257$ and $329$ so as to leave a remainder $5$ in each case.

Answer 1

Let $x=257$

$y=329$

Given $R=5$

$\Rightarrow x-5=257-5=252$

$\Rightarrow y-5=329-5=324$

Factorize $252$ and $324$

$252=2^2\times 3^2\times 7$

$324=2^2\times 3^4$

Required number will be the HCF of $324$ and $252$

$HCF=2^2\times 3^2=4\times 9=36$.