Prime factorization of $$$2682$$$

Find the prime factorization of $$$2682$$$.

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

Determine whether $$$2682$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2682$$$ by $$${\color{green}2}$$$: $$$\frac{2682}{2} = {\color{red}1341}$$$.

Determine whether $$$1341$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1341$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1341$$$ by $$${\color{green}3}$$$: $$$\frac{1341}{3} = {\color{red}447}$$$.

Determine whether $$$447$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$447$$$ by $$${\color{green}3}$$$: $$$\frac{447}{3} = {\color{red}149}$$$.

The prime number $$${\color{green}149}$$$ has no other factors then $$$1$$$ and $$${\color{green}149}$$$: $$$\frac{149}{149} = {\color{red}1}$$$.

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: $$$2682 = 2 \cdot 3^{2} \cdot 149$$$.

The prime factorization is $$$2682 = 2 \cdot 3^{2} \cdot 149$$$A.