Question 50

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

Solution

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

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

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

Share on Whatsapp Share on Whatsapp

Follow us on

Boost your Prep!

Download App