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Question
The difference of a two-digit number and the number obtained by reversing its digits is always divisible by ______.
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Solution
The difference of a two-digit number and the number obtained by reversing its digits is always divisible by 9.
Explanation:
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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