Prime factorization of $$$4332$$$

Find the prime factorization of $$$4332$$$.

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

Determine whether $$$4332$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4332$$$ by $$${\color{green}2}$$$: $$$\frac{4332}{2} = {\color{red}2166}$$$.

Determine whether $$$2166$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2166$$$ by $$${\color{green}2}$$$: $$$\frac{2166}{2} = {\color{red}1083}$$$.

Determine whether $$$1083$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1083$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1083$$$ by $$${\color{green}3}$$$: $$$\frac{1083}{3} = {\color{red}361}$$$.

Determine whether $$$361$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$361$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$361$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$361$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$361$$$ is divisible by $$$13$$$.

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

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

Determine whether $$$361$$$ is divisible by $$$17$$$.

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

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

Determine whether $$$361$$$ is divisible by $$$19$$$.

It is divisible, thus, divide $$$361$$$ by $$${\color{green}19}$$$: $$$\frac{361}{19} = {\color{red}19}$$$.

The prime number $$${\color{green}19}$$$ has no other factors then $$$1$$$ and $$${\color{green}19}$$$: $$$\frac{19}{19} = {\color{red}1}$$$.

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: $$$4332 = 2^{2} \cdot 3 \cdot 19^{2}$$$.

The prime factorization is $$$4332 = 2^{2} \cdot 3 \cdot 19^{2}$$$A.