Prime factorization of $$$2322$$$

Find the prime factorization of $$$2322$$$.

Start with the number $$$2$$$.

Determine whether $$$2322$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2322$$$ by $$${\color{green}2}$$$: $$$\frac{2322}{2} = {\color{red}1161}$$$.

Determine whether $$$1161$$$ is divisible by $$$2$$$.

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

The next prime number is $$$3$$$.

Determine whether $$$1161$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1161$$$ by $$${\color{green}3}$$$: $$$\frac{1161}{3} = {\color{red}387}$$$.

Determine whether $$$387$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$387$$$ by $$${\color{green}3}$$$: $$$\frac{387}{3} = {\color{red}129}$$$.

Determine whether $$$129$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$129$$$ by $$${\color{green}3}$$$: $$$\frac{129}{3} = {\color{red}43}$$$.

The prime number $$${\color{green}43}$$$ has no other factors then $$$1$$$ and $$${\color{green}43}$$$: $$$\frac{43}{43} = {\color{red}1}$$$.

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: $$$2322 = 2 \cdot 3^{3} \cdot 43$$$.

The prime factorization is $$$2322 = 2 \cdot 3^{3} \cdot 43$$$A.