Question 50

The sum of the reciprocals of the positive divisiors of 120 is

$$120 = 2 * 2 * 2 * 3 * 5 = 2^3 * 3^1 * 5^1$$

Sum of factors = $$(2^0 + 2^1 +Β 2^2 +Β 2^3) *Β (3^0 * 3^1) * (5^0 * 5^1) = (1 + 2 +Β 4 + 8) * (1 +Β 3) * (1 +Β 5) = 15 * 4 * 6 = 360$$

Ssum of the reciprocals factors = $$\frac{360}{120} = 3$$

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