Prime factorization of $$$2022$$$

Find the prime factorization of $$$2022$$$.

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

Determine whether $$$2022$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2022$$$ by $$${\color{green}2}$$$: $$$\frac{2022}{2} = {\color{red}1011}$$$.

Determine whether $$$1011$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1011$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1011$$$ by $$${\color{green}3}$$$: $$$\frac{1011}{3} = {\color{red}337}$$$.

The prime number $$${\color{green}337}$$$ has no other factors then $$$1$$$ and $$${\color{green}337}$$$: $$$\frac{337}{337} = {\color{red}1}$$$.

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: $$$2022 = 2 \cdot 3 \cdot 337$$$.

The prime factorization is $$$2022 = 2 \cdot 3 \cdot 337$$$A.