Prime factorization of $$$4689$$$

Find the prime factorization of $$$4689$$$.

Start with the number $$$2$$$.

Determine whether $$$4689$$$ is divisible by $$$2$$$.

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

The next prime number is $$$3$$$.

Determine whether $$$4689$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$4689$$$ by $$${\color{green}3}$$$: $$$\frac{4689}{3} = {\color{red}1563}$$$.

Determine whether $$$1563$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1563$$$ by $$${\color{green}3}$$$: $$$\frac{1563}{3} = {\color{red}521}$$$.

The prime number $$${\color{green}521}$$$ has no other factors then $$$1$$$ and $$${\color{green}521}$$$: $$$\frac{521}{521} = {\color{red}1}$$$.

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: $$$4689 = 3^{2} \cdot 521$$$.

The prime factorization is $$$4689 = 3^{2} \cdot 521$$$A.