Prime factorization of $$$4324$$$

Find the prime factorization of $$$4324$$$.

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

Determine whether $$$4324$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4324$$$ by $$${\color{green}2}$$$: $$$\frac{4324}{2} = {\color{red}2162}$$$.

Determine whether $$$2162$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2162$$$ by $$${\color{green}2}$$$: $$$\frac{2162}{2} = {\color{red}1081}$$$.

Determine whether $$$1081$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1081$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1081$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$1081$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$1081$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$1081$$$ is divisible by $$$13$$$.

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

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

Determine whether $$$1081$$$ is divisible by $$$17$$$.

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

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

Determine whether $$$1081$$$ is divisible by $$$19$$$.

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

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

Determine whether $$$1081$$$ is divisible by $$$23$$$.

It is divisible, thus, divide $$$1081$$$ by $$${\color{green}23}$$$: $$$\frac{1081}{23} = {\color{red}47}$$$.

The prime number $$${\color{green}47}$$$ has no other factors then $$$1$$$ and $$${\color{green}47}$$$: $$$\frac{47}{47} = {\color{red}1}$$$.

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: $$$4324 = 2^{2} \cdot 23 \cdot 47$$$.

The prime factorization is $$$4324 = 2^{2} \cdot 23 \cdot 47$$$A.