# Prime factorization of $4608$

The calculator will find the prime factorization of $4608$, with steps shown.

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Find the prime factorization of $4608$.

### Solution

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.