# Prime factorization of $2022$

The calculator will find the prime factorization of $2022$, with steps shown.

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Find the prime factorization of $2022$.

### Solution

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.