# Prime factorization of $4509$

The calculator will find the prime factorization of $4509$, with steps shown.

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Find the prime factorization of $4509$.

### Solution

Start with the number $2$.

Determine whether $4509$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $4509$ is divisible by $3$.

It is divisible, thus, divide $4509$ by ${\color{green}3}$: $\frac{4509}{3} = {\color{red}1503}$.

Determine whether $1503$ is divisible by $3$.

It is divisible, thus, divide $1503$ by ${\color{green}3}$: $\frac{1503}{3} = {\color{red}501}$.

Determine whether $501$ is divisible by $3$.

It is divisible, thus, divide $501$ by ${\color{green}3}$: $\frac{501}{3} = {\color{red}167}$.

The prime number ${\color{green}167}$ has no other factors then $1$ and ${\color{green}167}$: $\frac{167}{167} = {\color{red}1}$.

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: $4509 = 3^{3} \cdot 167$.

The prime factorization is $4509 = 3^{3} \cdot 167$A.