# Prime factorization of $1584$

The calculator will find the prime factorization of $1584$, with steps shown.

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Find the prime factorization of $1584$.

### Solution

Start with the number $2$.

Determine whether $1584$ is divisible by $2$.

It is divisible, thus, divide $1584$ by ${\color{green}2}$: $\frac{1584}{2} = {\color{red}792}$.

Determine whether $792$ is divisible by $2$.

It is divisible, thus, divide $792$ by ${\color{green}2}$: $\frac{792}{2} = {\color{red}396}$.

Determine whether $396$ is divisible by $2$.

It is divisible, thus, divide $396$ by ${\color{green}2}$: $\frac{396}{2} = {\color{red}198}$.

Determine whether $198$ is divisible by $2$.

It is divisible, thus, divide $198$ by ${\color{green}2}$: $\frac{198}{2} = {\color{red}99}$.

Determine whether $99$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $99$ is divisible by $3$.

It is divisible, thus, divide $99$ by ${\color{green}3}$: $\frac{99}{3} = {\color{red}33}$.

Determine whether $33$ is divisible by $3$.

It is divisible, thus, divide $33$ by ${\color{green}3}$: $\frac{33}{3} = {\color{red}11}$.

The prime number ${\color{green}11}$ has no other factors then $1$ and ${\color{green}11}$: $\frac{11}{11} = {\color{red}1}$.

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: $1584 = 2^{4} \cdot 3^{2} \cdot 11$.

The prime factorization is $1584 = 2^{4} \cdot 3^{2} \cdot 11$A.