Prime factorization of $$$4389$$$

Find the prime factorization of $$$4389$$$.

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

Determine whether $$$4389$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$4389$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$4389$$$ by $$${\color{green}3}$$$: $$$\frac{4389}{3} = {\color{red}1463}$$$.

Determine whether $$$1463$$$ is divisible by $$$3$$$.

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

The next prime number is $$$5$$$.

Determine whether $$$1463$$$ is divisible by $$$5$$$.

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

The next prime number is $$$7$$$.

Determine whether $$$1463$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$1463$$$ by $$${\color{green}7}$$$: $$$\frac{1463}{7} = {\color{red}209}$$$.

Determine whether $$$209$$$ is divisible by $$$7$$$.

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

The next prime number is $$$11$$$.

Determine whether $$$209$$$ is divisible by $$$11$$$.

It is divisible, thus, divide $$$209$$$ by $$${\color{green}11}$$$: $$$\frac{209}{11} = {\color{red}19}$$$.

The prime number $$${\color{green}19}$$$ has no other factors then $$$1$$$ and $$${\color{green}19}$$$: $$$\frac{19}{19} = {\color{red}1}$$$.

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: $$$4389 = 3 \cdot 7 \cdot 11 \cdot 19$$$.

The prime factorization is $$$4389 = 3 \cdot 7 \cdot 11 \cdot 19$$$A.