Question

Find the greatest number which divides $399,434$ & $537$ leaving the remainder $8,9$ & $10$ respectively.

Answer 1

The number divides $399,434$ and $537$ leaving the remainder $8,9$ and $10$.

So, that number will divide $(399-8),(434-9)$ and $(537-10)$ completely.

Now, the greatest number that will divide $391,425$ and $527$ completely, is the H.C.F. of these numbers.

$391=17\times 23$

$425=5\times 5\times 17$

$527=17\times 31$

H.C.F. $=17$