Prime factorization of $$$2982$$$

Find the prime factorization of $$$2982$$$.

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

Determine whether $$$2982$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2982$$$ by $$${\color{green}2}$$$: $$$\frac{2982}{2} = {\color{red}1491}$$$.

Determine whether $$$1491$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1491$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1491$$$ by $$${\color{green}3}$$$: $$$\frac{1491}{3} = {\color{red}497}$$$.

Determine whether $$$497$$$ is divisible by $$$3$$$.

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

The next prime number is $$$5$$$.

Determine whether $$$497$$$ is divisible by $$$5$$$.

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

The next prime number is $$$7$$$.

Determine whether $$$497$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$497$$$ by $$${\color{green}7}$$$: $$$\frac{497}{7} = {\color{red}71}$$$.

The prime number $$${\color{green}71}$$$ has no other factors then $$$1$$$ and $$${\color{green}71}$$$: $$$\frac{71}{71} = {\color{red}1}$$$.

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: $$$2982 = 2 \cdot 3 \cdot 7 \cdot 71$$$.

The prime factorization is $$$2982 = 2 \cdot 3 \cdot 7 \cdot 71$$$A.