Factors Galore!
Let and denote the smallest positive integer with 7, 8 and 9 factors respectively. Find .
The answer is 124.
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1 solution
smallest number with seven factors: 7 = 7x1
so the only possibilities to become smallest is 2^6(3^0) = 64
smallest number with 8 factors: 8 = 2x2x2
8 = 4x2
8 = 8x1
then the least of the following:
(2^1)(3^1)(5^1) = 30
(2^3)(3^1) = 24
(2^7)(3^0) = 128
so the smallest is 24
smallest number with 9 factors:
9 = 3x3
9 = 9x1
the smallest should be ( 2^2)(3^2) = 36
A = 64,B = 24, C = 36
A + B + C = 64 + 24 + 36 = 124