# Prime factorization of $$$4509$$$

### Your Input

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

### Answer

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