find the largest number that will divide 398,436,542 leaving remainders 7,11,15 respectively

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- Jul 14th 2008, 09:59 PM #1

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- Jul 14th 2008, 10:01 PM #2

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- Jul 14th 2008, 10:17 PM #3
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