# Prime factorization of $4167$

The calculator will find the prime factorization of $4167$, 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 $4167$.

### Solution

Start with the number $2$.

Determine whether $4167$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $4167$ is divisible by $3$.

It is divisible, thus, divide $4167$ by ${\color{green}3}$: $\frac{4167}{3} = {\color{red}1389}$.

Determine whether $1389$ is divisible by $3$.

It is divisible, thus, divide $1389$ by ${\color{green}3}$: $\frac{1389}{3} = {\color{red}463}$.

The prime number ${\color{green}463}$ has no other factors then $1$ and ${\color{green}463}$: $\frac{463}{463} = {\color{red}1}$.

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: $4167 = 3^{2} \cdot 463$.

The prime factorization is $4167 = 3^{2} \cdot 463$A.