Prime factorization of $$$3162$$$

Find the prime factorization of $$$3162$$$.

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

Determine whether $$$3162$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3162$$$ by $$${\color{green}2}$$$: $$$\frac{3162}{2} = {\color{red}1581}$$$.

Determine whether $$$1581$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1581$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1581$$$ by $$${\color{green}3}$$$: $$$\frac{1581}{3} = {\color{red}527}$$$.

Determine whether $$$527$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$527$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$527$$$ is divisible by $$$7$$$.

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

The next prime number is $$$11$$$.

Determine whether $$$527$$$ is divisible by $$$11$$$.

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

The next prime number is $$$13$$$.

Determine whether $$$527$$$ is divisible by $$$13$$$.

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

The next prime number is $$$17$$$.

Determine whether $$$527$$$ is divisible by $$$17$$$.

It is divisible, thus, divide $$$527$$$ by $$${\color{green}17}$$$: $$$\frac{527}{17} = {\color{red}31}$$$.

The prime number $$${\color{green}31}$$$ has no other factors then $$$1$$$ and $$${\color{green}31}$$$: $$$\frac{31}{31} = {\color{red}1}$$$.

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: $$$3162 = 2 \cdot 3 \cdot 17 \cdot 31$$$.

The prime factorization is $$$3162 = 2 \cdot 3 \cdot 17 \cdot 31$$$A.