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

1. 4
2. 7
3. 9
4. 13

Correct answer: 4

Solution

If a number leaves the same remainder on dividing 43, 91, and 183, then it must divide their pairwise differences. These differences are 48, 92, and 140, whose HCF is 4. Hence the greatest such number is 4.

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