Prime factorization of $$$4692$$$

Find the prime factorization of $$$4692$$$.

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

Determine whether $$$4692$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4692$$$ by $$${\color{green}2}$$$: $$$\frac{4692}{2} = {\color{red}2346}$$$.

Determine whether $$$2346$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2346$$$ by $$${\color{green}2}$$$: $$$\frac{2346}{2} = {\color{red}1173}$$$.

Determine whether $$$1173$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1173$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1173$$$ by $$${\color{green}3}$$$: $$$\frac{1173}{3} = {\color{red}391}$$$.

Determine whether $$$391$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$391$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$391$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$391$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$391$$$ is divisible by $$$13$$$.

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

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

Determine whether $$$391$$$ is divisible by $$$17$$$.

It is divisible, thus, divide $$$391$$$ by $$${\color{green}17}$$$: $$$\frac{391}{17} = {\color{red}23}$$$.

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: $$$4692 = 2^{2} \cdot 3 \cdot 17 \cdot 23$$$.

The prime factorization is $$$4692 = 2^{2} \cdot 3 \cdot 17 \cdot 23$$$A.