Prime factorization of $$$4232$$$

Find the prime factorization of $$$4232$$$.

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

Determine whether $$$4232$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4232$$$ by $$${\color{green}2}$$$: $$$\frac{4232}{2} = {\color{red}2116}$$$.

Determine whether $$$2116$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2116$$$ by $$${\color{green}2}$$$: $$$\frac{2116}{2} = {\color{red}1058}$$$.

Determine whether $$$1058$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1058$$$ by $$${\color{green}2}$$$: $$$\frac{1058}{2} = {\color{red}529}$$$.

Determine whether $$$529$$$ is divisible by $$$2$$$.

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

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

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: $$$4232 = 2^{3} \cdot 23^{2}$$$.

The prime factorization is $$$4232 = 2^{3} \cdot 23^{2}$$$A.