Prime factorization of $$$3804$$$

Find the prime factorization of $$$3804$$$.

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

Determine whether $$$3804$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3804$$$ by $$${\color{green}2}$$$: $$$\frac{3804}{2} = {\color{red}1902}$$$.

Determine whether $$$1902$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1902$$$ by $$${\color{green}2}$$$: $$$\frac{1902}{2} = {\color{red}951}$$$.

Determine whether $$$951$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$951$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$951$$$ by $$${\color{green}3}$$$: $$$\frac{951}{3} = {\color{red}317}$$$.

The prime number $$${\color{green}317}$$$ has no other factors then $$$1$$$ and $$${\color{green}317}$$$: $$$\frac{317}{317} = {\color{red}1}$$$.

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: $$$3804 = 2^{2} \cdot 3 \cdot 317$$$.

The prime factorization is $$$3804 = 2^{2} \cdot 3 \cdot 317$$$A.