Prime factorization of $$$4608$$$

Find the prime factorization of $$$4608$$$.

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

Determine whether $$$4608$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4608$$$ by $$${\color{green}2}$$$: $$$\frac{4608}{2} = {\color{red}2304}$$$.

Determine whether $$$2304$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2304$$$ by $$${\color{green}2}$$$: $$$\frac{2304}{2} = {\color{red}1152}$$$.

Determine whether $$$1152$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1152$$$ by $$${\color{green}2}$$$: $$$\frac{1152}{2} = {\color{red}576}$$$.

Determine whether $$$576$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$576$$$ by $$${\color{green}2}$$$: $$$\frac{576}{2} = {\color{red}288}$$$.

Determine whether $$$288$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$288$$$ by $$${\color{green}2}$$$: $$$\frac{288}{2} = {\color{red}144}$$$.

Determine whether $$$144$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$144$$$ by $$${\color{green}2}$$$: $$$\frac{144}{2} = {\color{red}72}$$$.

Determine whether $$$72$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$72$$$ by $$${\color{green}2}$$$: $$$\frac{72}{2} = {\color{red}36}$$$.

Determine whether $$$36$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$36$$$ by $$${\color{green}2}$$$: $$$\frac{36}{2} = {\color{red}18}$$$.

Determine whether $$$18$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$18$$$ by $$${\color{green}2}$$$: $$$\frac{18}{2} = {\color{red}9}$$$.

Determine whether $$$9$$$ is divisible by $$$2$$$.

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

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

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: $$$4608 = 2^{9} \cdot 3^{2}$$$.

The prime factorization is $$$4608 = 2^{9} \cdot 3^{2}$$$A.