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Question

The digits of a two-digit number AB are reversed to form a second two-digit number, and the lesser of the two-digit numbers is subtracted from the greater. What prime number must be a factor of the difference if A B?

Accepted Answer

AB -BA= 10 A+B - (10 B+A)= 9 A-9 B=3(3 A-3 B). If A B, then the difference is a (non-zero) multiple of 3. Thus, 3 must be a factor of AB -BA.