Prime factorization of $$$3264$$$

Find the prime factorization of $$$3264$$$.

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

Determine whether $$$3264$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3264$$$ by $$${\color{green}2}$$$: $$$\frac{3264}{2} = {\color{red}1632}$$$.

Determine whether $$$1632$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1632$$$ by $$${\color{green}2}$$$: $$$\frac{1632}{2} = {\color{red}816}$$$.

Determine whether $$$816$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$816$$$ by $$${\color{green}2}$$$: $$$\frac{816}{2} = {\color{red}408}$$$.

Determine whether $$$408$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$408$$$ by $$${\color{green}2}$$$: $$$\frac{408}{2} = {\color{red}204}$$$.

Determine whether $$$204$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$204$$$ by $$${\color{green}2}$$$: $$$\frac{204}{2} = {\color{red}102}$$$.

Determine whether $$$102$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$102$$$ by $$${\color{green}2}$$$: $$$\frac{102}{2} = {\color{red}51}$$$.

Determine whether $$$51$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$51$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$51$$$ by $$${\color{green}3}$$$: $$$\frac{51}{3} = {\color{red}17}$$$.

The prime number $$${\color{green}17}$$$ has no other factors then $$$1$$$ and $$${\color{green}17}$$$: $$$\frac{17}{17} = {\color{red}1}$$$.

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: $$$3264 = 2^{6} \cdot 3 \cdot 17$$$.

The prime factorization is $$$3264 = 2^{6} \cdot 3 \cdot 17$$$A.