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Question
The difference of three-digit number and the number obtained by putting the digits in reverse order is always divisible by 9 and ______.
Solution
The difference of three-digit number and the number obtained by putting the digits in reverse order is always divisible by 9 and 11.
Explanation:
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 × 11 × (a – c)
Hence, abc – cba is always divisible by 9, 11 and (a – c).
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