Question

Find the largest number that will divide $398,436$ and $542$ leaving remainders $7,11$ and $15$ respectively.

Answer 1

Clearly, the required number is the $HCF$ of the numbers $398-7=391,436-11=425,$ and, $542-15=527$.

First we find the $HCF$ of $391$ and $425$ by Euclids algorithm as given below.

Clearly, $H.C.F.$ of $391$ and $425$ is $17$.
Let us now the $HCF$ of $17$ and the third number $527$ by Euclids algorithm:

The $HCF$ of $17$ and $527$ is $17$. Hence, $HCF$ of $391,4250$ and $527$ is $17$.
Hence, the required number is $17$.