The difference of two-digit number

Question:

The difference of two-digit number and the number obtained by reversing its digits is always divisible by ———-.

Solution:

 9

Let ab be any two-digit number, then we have

ab – ba = (10a + b)- (10b + a)

= 9a – 9b = 9(a – b)

Hence, ab – ba is always divisible by 9 and (a – b).

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