Question

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

Answer 1

${\huge{\underbrace{\overbrace{\color{aqua}{Question:-}}}}}$

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

$\huge\mathfrak\red{❥Solution:-}$

Let x=257

y=329

Given R=5

⇒x−5=257−5⇒252

⇒y−5=329−5⇒324

Factorize 252 & 324

$252 = {2}^{2} \times {3}^{2} \times 7 \\ 324 = {2}^{2} \times {3}^{4} \\ G.C.F⇒ {2}^{2} \times {3}^{2} = 4 \times 9 = 36$

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