Prime factorization of $$$3663$$$

Find the prime factorization of $$$3663$$$.

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

Determine whether $$$3663$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$3663$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$3663$$$ by $$${\color{green}3}$$$: $$$\frac{3663}{3} = {\color{red}1221}$$$.

Determine whether $$$1221$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1221$$$ by $$${\color{green}3}$$$: $$$\frac{1221}{3} = {\color{red}407}$$$.

Determine whether $$$407$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$407$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$407$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$407$$$ is divisible by $$$11$$$.

It is divisible, thus, divide $$$407$$$ by $$${\color{green}11}$$$: $$$\frac{407}{11} = {\color{red}37}$$$.

The prime number $$${\color{green}37}$$$ has no other factors then $$$1$$$ and $$${\color{green}37}$$$: $$$\frac{37}{37} = {\color{red}1}$$$.

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: $$$3663 = 3^{2} \cdot 11 \cdot 37$$$.

The prime factorization is $$$3663 = 3^{2} \cdot 11 \cdot 37$$$A.