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Question

# Find the greatest number that will divide 43,91 and 183 so as to leave the same remainder in each case.47139

A
9
B
13
C
4
D
7
Solution
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#### 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=2×2×2×392=2×2×23140=2×2×5×7The greatest common divisor of {48,92,140} is 4. So, answer is 4.

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