Question

56. By what greatest number 162, 382 and 877 must be divided, so that
remainder in each case will be less than the divisor by 3 ?​

Answer 1

Answer with Step-by-step explanation:

The last line in the question is superfluous and has no role in determining the answer. The question can be restated as find greatest number that divides 162, 382 & 877 leaving same remainder in each case.

Effectively, we are required to find :

HCF(382 - 162, 877 - 382)

220 = 2 x 2 x 5 x 11

495 = 3 x 3 x 5 x 11

HCF(220,495) = 55

[ Remainder 162/55 = 52

Remainder 382/55 = 52

Remainder 877/55 = 52 ]

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