Question

The sum of two number is $528$ and their $H.C.F$ is $33$. What is the number of pairs of such numbers?

Answer 1

Let the numbers are $33x,33y$

and given that $HCM=33$

$33(x+y)=528$

$x+y=16$

When

$x=33,y=495$

$x=66,y=462$

$x=99,y=429$

$x=132,y=397$

Hence, there are 4 possible pairs.