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