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Question
Let abc be a three-digit number. Then abc – cba is not divisible by ______.
Options
9
11
18
33
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Solution
Let abc be a three-digit number. Then abc – cba is not divisible by 18.
Explanation:
Given, abc is a three-digit number.
Then, abc = 100a + 10b + c
And cba = 100c + 10b + a
abc – cba = (100a + 10b + c) – (100c + 10b + a)
= 100a – a + 10b – 10b + c – 100
= 99a – 99c
= 99(a – c)
= abc – cba is divisible by 99.
⇒ abc – cba is divisible by 9, 11, 33, but it is not divisible by 18.
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