# Prime factorization of $4023$

The calculator will find the prime factorization of $4023$, with steps shown.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Find the prime factorization of $4023$.

### Solution

Start with the number $2$.

Determine whether $4023$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $4023$ is divisible by $3$.

It is divisible, thus, divide $4023$ by ${\color{green}3}$: $\frac{4023}{3} = {\color{red}1341}$.

Determine whether $1341$ is divisible by $3$.

It is divisible, thus, divide $1341$ by ${\color{green}3}$: $\frac{1341}{3} = {\color{red}447}$.

Determine whether $447$ is divisible by $3$.

It is divisible, thus, divide $447$ by ${\color{green}3}$: $\frac{447}{3} = {\color{red}149}$.

The prime number ${\color{green}149}$ has no other factors then $1$ and ${\color{green}149}$: $\frac{149}{149} = {\color{red}1}$.

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: $4023 = 3^{3} \cdot 149$.

The prime factorization is $4023 = 3^{3} \cdot 149$A.