Prime factorization of $$$2118$$$

Find the prime factorization of $$$2118$$$.

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

Determine whether $$$2118$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2118$$$ by $$${\color{green}2}$$$: $$$\frac{2118}{2} = {\color{red}1059}$$$.

Determine whether $$$1059$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1059$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1059$$$ by $$${\color{green}3}$$$: $$$\frac{1059}{3} = {\color{red}353}$$$.

The prime number $$${\color{green}353}$$$ has no other factors then $$$1$$$ and $$${\color{green}353}$$$: $$$\frac{353}{353} = {\color{red}1}$$$.

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: $$$2118 = 2 \cdot 3 \cdot 353$$$.

The prime factorization is $$$2118 = 2 \cdot 3 \cdot 353$$$A.