how to count the number of tree factor?

Question

example
input
2
output
2 1
3 1

// from 6=2×3
// there are one 2 and one 3

input
60
output
2 2
3 1
5 1

// from 60=2×2×3×5
//there are two 2, one 3, and one 5

Answer 1

Get all prime numbers with the Sieve of Eratosthenes, that are below your number divided by 2.

Lets take a look at your example with 60:
The prims below you are looking for are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

Take the first prime number:
60 mod 2 == 0 => 2 1
60 / 2 = 30

Repeat with 30:
30 mod 2 == 0 => 2 2
30 / 2 = 15

Repeat with 15:
15 mod 2 != 0 => next prime number
15 mod 3 ==0 => 2 2, 3 1
15 / 3 = 5

Repeat with 5:
5 mod 3 != 0 => next prime number
5 mod 5 ==0 => 2 2, 3 1, 5 1
5 / 5 = 1 => DONE