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

Foundation

Mathematics Foundation

HCF and LCM

Properties of Real Number

Rational Numbers

Question

Find the greatest number which can divide

257

and

329

so as to leave a remainder

5

in each case.

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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

H C F = 2^{2} \times 3^{2} = 4 \times 9 = 36