# Prime factorization of $2313$

The calculator will find the prime factorization of $2313$, with steps shown.

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Find the prime factorization of $2313$.

### Solution

Start with the number $2$.

Determine whether $2313$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2313$ is divisible by $3$.

It is divisible, thus, divide $2313$ by ${\color{green}3}$: $\frac{2313}{3} = {\color{red}771}$.

Determine whether $771$ is divisible by $3$.

It is divisible, thus, divide $771$ by ${\color{green}3}$: $\frac{771}{3} = {\color{red}257}$.

The prime number ${\color{green}257}$ has no other factors then $1$ and ${\color{green}257}$: $\frac{257}{257} = {\color{red}1}$.

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: $2313 = 3^{2} \cdot 257$.

The prime factorization is $2313 = 3^{2} \cdot 257$A.