Let abc be a three-digit number. Then abc – cba is not divisible by


General form of abc is 100a + 10b + c and general form of cba is 100c + 10b + a .

Now abc – cba = (100a + 10b + c) – (100c + 10b + a)


abc – cba = 100a – a + 10b – 10b + c – 100c.


abc – cba = 99a -99c = 99(a-c)


abc – cba is divisible by 99 because 99 is factor of abc – cba.


Hence all numbers which are factors of 99 will also be divisible by abc – cba.


Option (a) 9 is the factor of 99 ( 11 x 9 = 99). Therefore abc-cba is divisible by 9.


Option (b) 11 is the factor of 99 ( 11 x 9 = 99). Therefore abc-cba is divisible by 11


Option (c) 18 is not the factor of 99 because does not give 0 remainder. Therefore abc - cba is not divisible by 18.


Option (d) 33 is the factor of 99 (33 x 3 = 99). Therefore abc-cba is divisible by 33.

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