The difference of three-digit number and the number obtained by putting the digits in reverse order is always divisible by 9 and——-.
Let abc be a three-digit number, then we have
abc -cba = (100a + 10b + c)- (100c + 10b+ a) ; = (100a – a) + (c – 10Cc)
= 99a – 99c = 99(a -c)
= 9 x 11 x (a – c)
Hence, abc – cba is always divisible by 9,11 and (a – c).