Prime factorization of $$$2334$$$

Find the prime factorization of $$$2334$$$.

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

Determine whether $$$2334$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2334$$$ by $$${\color{green}2}$$$: $$$\frac{2334}{2} = {\color{red}1167}$$$.

Determine whether $$$1167$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1167$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1167$$$ by $$${\color{green}3}$$$: $$$\frac{1167}{3} = {\color{red}389}$$$.

The prime number $$${\color{green}389}$$$ has no other factors then $$$1$$$ and $$${\color{green}389}$$$: $$$\frac{389}{389} = {\color{red}1}$$$.

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: $$$2334 = 2 \cdot 3 \cdot 389$$$.

The prime factorization is $$$2334 = 2 \cdot 3 \cdot 389$$$A.