Question

14. The greatest number that will divide 43, 106 and 124, so as to leave the same remainder in each case would be
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Answer 1

4

Step-by-step explanation:

Here, we need to find differences between the given numbers. If two numbers give the same remainder when divided by some other number, then their difference must give a remainder of zero when divided by that number.

Our numbers here are 91−43=48,183−91=92,183−43=140

So we have the set of numbers {48,92,140} and we want to know the biggest number that divides all these numbers.

So,

48=2×2×2×3

92=2×2×23

140=2×2×5×7

The greatest common divisor of {48,92,140} is 4.

So, answer is 4.