Prime factorization of $$$3174$$$

Find the prime factorization of $$$3174$$$.

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

Determine whether $$$3174$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3174$$$ by $$${\color{green}2}$$$: $$$\frac{3174}{2} = {\color{red}1587}$$$.

Determine whether $$$1587$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1587$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1587$$$ by $$${\color{green}3}$$$: $$$\frac{1587}{3} = {\color{red}529}$$$.

Determine whether $$$529$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$529$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$529$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$529$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$529$$$ is divisible by $$$13$$$.

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

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

Determine whether $$$529$$$ is divisible by $$$17$$$.

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

The next prime number is $$$19$$$.

Determine whether $$$529$$$ is divisible by $$$19$$$.

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

The next prime number is $$$23$$$.

Determine whether $$$529$$$ is divisible by $$$23$$$.

It is divisible, thus, divide $$$529$$$ by $$${\color{green}23}$$$: $$$\frac{529}{23} = {\color{red}23}$$$.

The prime number $$${\color{green}23}$$$ has no other factors then $$$1$$$ and $$${\color{green}23}$$$: $$$\frac{23}{23} = {\color{red}1}$$$.

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: $$$3174 = 2 \cdot 3 \cdot 23^{2}$$$.

The prime factorization is $$$3174 = 2 \cdot 3 \cdot 23^{2}$$$A.