Question

if N = 4728x5y is divisible by 24 then find the possible Values of |x,y|

Answer 1

do you mean N = 4728 * x^5 * y ?
well 4728 / 24 = 197
so if x = 1 and y = 1 that works
but what others might there be
4728= 197 * 24 = 197 *2*2*2*3
197 is a prime number
I do not see any x^5 y^1 that works, too bad it is not x^3 y^1

Answer 2

To be divisible by 24, it must divide by 8 AND 3
N must also be even, so y can only be 0, 2,4, 6, or 8
To be divisible by 8 the last 3 digits of a number must be divisible by 8
so the x5y part could only be
052, 152, 252, ... 952, 054, 154, ... 954, 056, 156, ..., 956, .... 958
A scan of these shows that 456 and 552 will work
so x = 4, y = 6 , then xy = 24
if x = 5, y = 2, then xy = 10

The two numbers are
4728456
and
4728552

It was easy to check that they also divide by 3