Question

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

Answer 1

$\underline{\underline{\pink{\sf Answer}}}$

☞ The Greatest number is 36

$\underline{\underline{\red{\sf Given}}}$

✭ The Numbers 257 and 329 are divided by a number

✭ And in both the case we get a remainder 5

$\underline{\underline{\green{\sf To \ Find}}}$

◈ The Number by which they are divided?

$\underline{\underline{\blue{\sf Steps}}}$

So here we shall first subtract 5 from both the numbers,

➢ 257 - 5 = 252

➢ 329 - 5 = 324

Assume that the unknown divisor is x, so it can be simply found by finding the HCF of 252 and 324

HCF(252,324)

➝ 252 = 2 × 2 × 3 × 3 × 7 = 2² × 3² × 7

➝ 324 = 2 × 2 × 3 × 3 × 3 × 3 = 2² × 3⁴

HCF is the product of the least power of the common factors so,

➳ HCF = 2² × 3²

➳ HCF = 4 × 9

➳ HCF(252,324) = 36

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