# 2.1 GCDs

## Unique Primes

1. How many prime factors does $$40500$$ have?

Exercise 1

2. How many unique prime factors does $$40500$$ have?

Exercise 2

The prime factorization of $$40500 = 2^2\cdot 3^4 \cdot 5^3$$, so it is composed of $$2+4+3$$ (non-unique) prime factors. However, only three of these are unique, namely $$2, 3$$ and $$4$$.