# Prime factorization of $4590$

The calculator will find the prime factorization of $4590$, with steps shown.

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Find the prime factorization of $4590$.

### Solution

Start with the number $2$.

Determine whether $4590$ is divisible by $2$.

It is divisible, thus, divide $4590$ by ${\color{green}2}$: $\frac{4590}{2} = {\color{red}2295}$.

Determine whether $2295$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2295$ is divisible by $3$.

It is divisible, thus, divide $2295$ by ${\color{green}3}$: $\frac{2295}{3} = {\color{red}765}$.

Determine whether $765$ is divisible by $3$.

It is divisible, thus, divide $765$ by ${\color{green}3}$: $\frac{765}{3} = {\color{red}255}$.

Determine whether $255$ is divisible by $3$.

It is divisible, thus, divide $255$ by ${\color{green}3}$: $\frac{255}{3} = {\color{red}85}$.

Determine whether $85$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $85$ is divisible by $5$.

It is divisible, thus, divide $85$ by ${\color{green}5}$: $\frac{85}{5} = {\color{red}17}$.

The prime number ${\color{green}17}$ has no other factors then $1$ and ${\color{green}17}$: $\frac{17}{17} = {\color{red}1}$.

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: $4590 = 2 \cdot 3^{3} \cdot 5 \cdot 17$.

The prime factorization is $4590 = 2 \cdot 3^{3} \cdot 5 \cdot 17$A.