For any integer the numbers
A. one of its factors
are two different integers except when the integer is a
perfect square and that factor is its square root.
So only perfect squares have an odd number of factors, since
its square root and %28that_perfect_square%29%2F%28its_square_root%29 are not two different
factors, but only one factor, since those are the same number.
So it has to be a perfect square to have 5 factors.
So it has to be one of these:
16, 25, 36, 49, 64, or 81
16 is not divisible by 1+6, which is 7
25 is not divisible by 2+5, which is 7
36 IS divisible by 3+6, which is 9. However 36 has
9 factors 1,2,3,4,6,9,12,18, and 36, and that's too many.
64 is not divisible by 6+4, which is 10.
81 is divisible by 8+1, which is 9. It's factors are 1,3,9,27, and 81.
And that's 5, so the number is 81.
Answer: The sum of the factors is 1+3+9+27+81 = 121
