Prime factorization of $$$3114$$$

Find the prime factorization of $$$3114$$$.

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

Determine whether $$$3114$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3114$$$ by $$${\color{green}2}$$$: $$$\frac{3114}{2} = {\color{red}1557}$$$.

Determine whether $$$1557$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1557$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1557$$$ by $$${\color{green}3}$$$: $$$\frac{1557}{3} = {\color{red}519}$$$.

Determine whether $$$519$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$519$$$ by $$${\color{green}3}$$$: $$$\frac{519}{3} = {\color{red}173}$$$.

The prime number $$${\color{green}173}$$$ has no other factors then $$$1$$$ and $$${\color{green}173}$$$: $$$\frac{173}{173} = {\color{red}1}$$$.

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: $$$3114 = 2 \cdot 3^{2} \cdot 173$$$.

The prime factorization is $$$3114 = 2 \cdot 3^{2} \cdot 173$$$A.