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Math Help - Least number which leaves remainder 1,2,3,4 when divided succesively by 2,3,5,7

  1. #1
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    Least number which leaves remainder 1,2,3,4 when divided succesively by 2,3,5,7

    Hi All,

    Please help me with this problem:

    What is the least number which leaves remainder 1, 2, 3 and 4 when divided successively by 2, 3, 5 and 7?

    Thank you,
    Ashwin Kumar D P.
    Bangalore, India.
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  2. #2
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    Quote Originally Posted by ashwinkumardp View Post
    Hi All,
    Please help me with this problem:
    What is the least number which leaves remainder 1, 2, 3 and 4 when divided successively by 2, 3, 5 and 7?
    Thank you,
    Ashwin Kumar D P.
    Bangalore, India.
    x \equiv 1 \mod 2 Equation1

    x \equiv 2 \mod 3 Equation2

    x \equiv 3 \mod 5 Equation3

    x \equiv 4 \mod 7 Equation4

    Use the Chinese Remainder Theorem.


    However, for this question try this:
    The values that satisfy Eqn4 are
    4, 11, 18, 25, 32, 39, ...
    They are 4 + multiples of 7.

    Use those values in Eqn3

    4 \equiv 4 \mod 5

    11 \equiv 1 \mod 5

    18 \equiv 3 \mod 5

    18 satisfies Eqn4 & Eqn3


    Use 18 + multiples of 35 ( 7 times 5 ) for Equation2
    18, 53, 88, 123, ...

    Find the one that satisfies equation2.
    Then a similar procedure for Equation1

    .
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