Prime factorization of $$$804$$$

Find the prime factorization of $$$804$$$.

Start with the number $$$2$$$.

Determine whether $$$804$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$804$$$ by $$${\color{green}2}$$$: $$$\frac{804}{2} = {\color{red}402}$$$.

Determine whether $$$402$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$402$$$ by $$${\color{green}2}$$$: $$$\frac{402}{2} = {\color{red}201}$$$.

Determine whether $$$201$$$ is divisible by $$$2$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$3$$$.

Determine whether $$$201$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$201$$$ by $$${\color{green}3}$$$: $$$\frac{201}{3} = {\color{red}67}$$$.

The prime number $$${\color{green}67}$$$ has no other factors then $$$1$$$ and $$${\color{green}67}$$$: $$$\frac{67}{67} = {\color{red}1}$$$.

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: $$$804 = 2^{2} \cdot 3 \cdot 67$$$.

The prime factorization is $$$804 = 2^{2} \cdot 3 \cdot 67$$$A.