Question 23

In the given question, fill in the blanks to make the statement true.

The difference of a three-digit number and the number obtained by putting the digits in reverse order is always divisible by 9 and ___.

11
Let abc be a three-digit number, then we have
abc - cba = (100a + 10b + c) - (100c + 10b + a)
= (100a - a) + (c - 100c)
= 99a - 99c
= 99(a - c)
= 9 $\times$ 11 $\times$ (a - c)
Hence, abc - cba is always divisible by 9, 11 and (a - c).