Prime factorization of $$$3432$$$

Find the prime factorization of $$$3432$$$.

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

Determine whether $$$3432$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3432$$$ by $$${\color{green}2}$$$: $$$\frac{3432}{2} = {\color{red}1716}$$$.

Determine whether $$$1716$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1716$$$ by $$${\color{green}2}$$$: $$$\frac{1716}{2} = {\color{red}858}$$$.

Determine whether $$$858$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$858$$$ by $$${\color{green}2}$$$: $$$\frac{858}{2} = {\color{red}429}$$$.

Determine whether $$$429$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$429$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$429$$$ by $$${\color{green}3}$$$: $$$\frac{429}{3} = {\color{red}143}$$$.

Determine whether $$$143$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$143$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$143$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$143$$$ is divisible by $$$11$$$.

It is divisible, thus, divide $$$143$$$ by $$${\color{green}11}$$$: $$$\frac{143}{11} = {\color{red}13}$$$.

The prime number $$${\color{green}13}$$$ has no other factors then $$$1$$$ and $$${\color{green}13}$$$: $$$\frac{13}{13} = {\color{red}1}$$$.

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: $$$3432 = 2^{3} \cdot 3 \cdot 11 \cdot 13$$$.

The prime factorization is $$$3432 = 2^{3} \cdot 3 \cdot 11 \cdot 13$$$A.