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912 – 512 is divisible by which of the following number?

912 – 512 is divisible by which of the following number? Correct Answer 106 or 56 or 14

We know that a3 – b3 = (a-b)(a2+b2+ab) and a2 – b2 = (a+b)(a-b). 912 – 512 = (94)3 – (54)3 = (94-54)(98+58+98*58) = (92-52)(92+52) (98+58+98*58) = (9+5)(9-5)(92+52)(98+58+98*58) 92-52=56, 9+5=14, 92+52=106. Hence, 912 – 512 is divisible by 106 or 56 or 14.

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