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Rajan@2021
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Guru

Find the largest four-digits number which when divided by 4, 7 and 13 leaves a remainder of 3 in each case.

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One of the most important and exam oriented question from real numbers in which we have been asked to find the largest four digits number which when divided by 4, 7 and 13 leaves a remainder of 3 in each case.

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 1B, question no 14

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1 Answer

  1. Prime factors of 4,7 and 13
    4=2×2

    7 and 13 are prime numbers
    LCM  (4,7,13)=364

    we know that, the largest 4 digit number is 9999.

    Step 1 : divide 9999 by 364, we get
    9999​/364=171

    Step 2: subtract 171 from 9999
    9999171=9828

    Since a remainder of 3 is to be left
    9282+3=9831

    therefore 9831 is the number.

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