# Prime factorization of $4584$

The calculator will find the prime factorization of $4584$, with steps shown.

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Find the prime factorization of $4584$.

### Solution

Start with the number $2$.

Determine whether $4584$ is divisible by $2$.

It is divisible, thus, divide $4584$ by ${\color{green}2}$: $\frac{4584}{2} = {\color{red}2292}$.

Determine whether $2292$ is divisible by $2$.

It is divisible, thus, divide $2292$ by ${\color{green}2}$: $\frac{2292}{2} = {\color{red}1146}$.

Determine whether $1146$ is divisible by $2$.

It is divisible, thus, divide $1146$ by ${\color{green}2}$: $\frac{1146}{2} = {\color{red}573}$.

Determine whether $573$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $573$ is divisible by $3$.

It is divisible, thus, divide $573$ by ${\color{green}3}$: $\frac{573}{3} = {\color{red}191}$.

The prime number ${\color{green}191}$ has no other factors then $1$ and ${\color{green}191}$: $\frac{191}{191} = {\color{red}1}$.

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: $4584 = 2^{3} \cdot 3 \cdot 191$.

The prime factorization is $4584 = 2^{3} \cdot 3 \cdot 191$A.