Find the greatest number that will divide 49, 97 and 189 so as to leave the same remainder in each case.

Correct option is B

Given:

Numbers: 49, 97, 189

Required: Greatest number that divides all three and leaves the same remainder.

Concept Used:

If a number leaves the same remainder when dividing multiple numbers, then it must divide the difference of those numbers.

Required number = HCF of differences.

Solution:

Differences:

97 - 49 = 48, 189 - 97 = 92, 189 - 49 = 140

HCF(48, 92, 140) = 4Thus, Greatest number that divides all three and leaves the same remainder is 4

Thus, Greatest number that divides all three and leaves the same remainder is 4