Prime factorization of $$$2313$$$

Find the prime factorization of $$$2313$$$.

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.