Prime factorization of $$$1989$$$

Find the prime factorization of $$$1989$$$.

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

Determine whether $$$1989$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1989$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1989$$$ by $$${\color{green}3}$$$: $$$\frac{1989}{3} = {\color{red}663}$$$.

Determine whether $$$663$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$663$$$ by $$${\color{green}3}$$$: $$$\frac{663}{3} = {\color{red}221}$$$.

Determine whether $$$221$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$221$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$221$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$221$$$ is divisible by $$$11$$$.

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

The next prime number is $$$13$$$.

Determine whether $$$221$$$ is divisible by $$$13$$$.

It is divisible, thus, divide $$$221$$$ by $$${\color{green}13}$$$: $$$\frac{221}{13} = {\color{red}17}$$$.

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: $$$1989 = 3^{2} \cdot 13 \cdot 17$$$.

The prime factorization is $$$1989 = 3^{2} \cdot 13 \cdot 17$$$A.