Prime factorization of $$$2004$$$
Your Input
Find the prime factorization of $$$2004$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$2004$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$2004$$$ by $$${\color{green}2}$$$: $$$\frac{2004}{2} = {\color{red}1002}$$$.
Determine whether $$$1002$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$1002$$$ by $$${\color{green}2}$$$: $$$\frac{1002}{2} = {\color{red}501}$$$.
Determine whether $$$501$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$501$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$501$$$ by $$${\color{green}3}$$$: $$$\frac{501}{3} = {\color{red}167}$$$.
The prime number $$${\color{green}167}$$$ has no other factors then $$$1$$$ and $$${\color{green}167}$$$: $$$\frac{167}{167} = {\color{red}1}$$$.
Since we have obtained $$$1$$$, we are done.
Now, just count the number of occurences of the divisors (green numbers), and write down the prime factorization: $$$2004 = 2^{2} \cdot 3 \cdot 167$$$.
Answer
The prime factorization is $$$2004 = 2^{2} \cdot 3 \cdot 167$$$A.