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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.

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This is the basic and conceptual question from real numbers in we have given three numbers 43, 91 and 183 and we have to find the greatest number that will divide the above number and leaves the same remainder in each case.

Kindly solve the above problem in detail.

RS Aggarwal, Class 10, chapter 1B, question no 16


1 Answer

  1. 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 9143=48,18391=92,18343=140
    So we have the set of numbers {48,92,140} and we want to know the biggest number that divides all these numbers.

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

    So, answer is 4.

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