Question

Harsh picks a three digit number and subtract it from the same number after reversing order of its digits. This difference will always be fully divisible by which of following number?

Answer 1

Step-by-step explanation: Difference of any three digit number by its reversing number is always a exact product of 9. i.e divisible by 9.

Let 100x+10y+z be the number; its reverse is 100z+10y+x.

Difference of the number will be:

(100x+10y+z)−(10z+10yb+x) = (100−1)x + (10−10)y + (1−100)z

= 99x−99z = 99(x−z)

So the difference of any three digit number with its reverse number is divisible by 9. ( Also 11 and 99)