Question

Let's call the number of prime factors of a natural number n, the "length". For example, the length of 12 = 2x2x3 which is length of three. How many positive integers less than 100 have a lenth of three?

Answer 1

Consider \(2\cdot 2 \cdot k = 4k <100\), therefore \(k < 25\).
You only have to consider prime numbers lower than \(25\).

Answer 2

For \(2\cdot 3\cdot k = 6k < 100\) we have \(k<16\)