Prime factorization of $$$3456$$$

Find the prime factorization of $$$3456$$$.

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

Determine whether $$$3456$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3456$$$ by $$${\color{green}2}$$$: $$$\frac{3456}{2} = {\color{red}1728}$$$.

Determine whether $$$1728$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1728$$$ by $$${\color{green}2}$$$: $$$\frac{1728}{2} = {\color{red}864}$$$.

Determine whether $$$864$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$864$$$ by $$${\color{green}2}$$$: $$$\frac{864}{2} = {\color{red}432}$$$.

Determine whether $$$432$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$432$$$ by $$${\color{green}2}$$$: $$$\frac{432}{2} = {\color{red}216}$$$.

Determine whether $$$216$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$216$$$ by $$${\color{green}2}$$$: $$$\frac{216}{2} = {\color{red}108}$$$.

Determine whether $$$108$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$108$$$ by $$${\color{green}2}$$$: $$$\frac{108}{2} = {\color{red}54}$$$.

Determine whether $$$54$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$54$$$ by $$${\color{green}2}$$$: $$$\frac{54}{2} = {\color{red}27}$$$.

Determine whether $$$27$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$27$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$27$$$ by $$${\color{green}3}$$$: $$$\frac{27}{3} = {\color{red}9}$$$.

Determine whether $$$9$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$9$$$ by $$${\color{green}3}$$$: $$$\frac{9}{3} = {\color{red}3}$$$.

The prime number $$${\color{green}3}$$$ has no other factors then $$$1$$$ and $$${\color{green}3}$$$: $$$\frac{3}{3} = {\color{red}1}$$$.

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: $$$3456 = 2^{7} \cdot 3^{3}$$$.

The prime factorization is $$$3456 = 2^{7} \cdot 3^{3}$$$A.