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Math Help - hcf

  1. #1
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    hcf

    find the largest number that will divide 398,436,542 leaving remainders 7,11,15 respectively
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  2. #2
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    [quote=dajinder;167011]find the largest number that will divide 398,436,542 leaving remainders 7,11,15 respectively
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  3. #3
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    Quote Originally Posted by dajinder View Post
    find the largest number that will divide 398,436,542 leaving remainders 7,11,15 respectively
    I will use the following fact:
    FACT: If a number 'm' leaves remainder 'r', when divided by 'n', then n divides m - r.

    Lets call the largest number that does the job as 'n'.

    So we want n|398 - 7,n|436 - 11,n|542 - 15.

    In other words we want the largest n such that n divides 391,425,527.

    The largest the number that divides the three numbers 391,425,527 is called the hcf of 391,425,527.

    Thus n = hcf(391,425,527) = 17
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