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By inspection, the number 7762 is indivisible by 3 (the sum of the digits is indivisible by 3 --> 7+7+6+2 = 22), 4 (the sum of the last two digits is indivisible by 4), 5 (the unit digit is not a 5 or 0), 7, and 11 (the sum of the odd digits does not equal to the sum of the even digits; 7+6 <> 7+2).

So far, I have 7762 = 2*3881.

Now we have to deal with 3881. We know any integer below 13 is not a divisor. I have tried all prime numbers by simple division up to 67. The square root of 3881 is 62.3, so no solution for 3881.

The factors are 1, 2 and 3881.

Q.E.D.

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12y ago

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