Question

How many natural numbers less than 50 have exactly 4 positive factors?

Options:
a) 13
b) 15
c) 17
d) 11

Answer 1

it’s letter D which means it’s 11

Answer 2

15

Explanation:

We will use the Tao function for our use. If there are 4 factors of a number then Tao function has a value of 4.

According to the Tao function, (a1 + 1)(a2 + 1).....(an + 1) = 4. So, by comparison We have two cases.

Case 1: a1 + 1 = 4

So, in that case a1 = 3 and we see there are two cubes less than 50.

Case 2: a1 + 1 = 2, a2 + 1 = 2

So, a1 = 1 and a2 = 1. Thus, it's a pure multiple of linear primes. And we notice there are 13 such numbers.