Prime factorization of $$$1443$$$

Find the prime factorization of $$$1443$$$.

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

Determine whether $$$1443$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1443$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1443$$$ by $$${\color{green}3}$$$: $$$\frac{1443}{3} = {\color{red}481}$$$.

Determine whether $$$481$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$481$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$481$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$481$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$481$$$ is divisible by $$$13$$$.

It is divisible, thus, divide $$$481$$$ by $$${\color{green}13}$$$: $$$\frac{481}{13} = {\color{red}37}$$$.

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: $$$1443 = 3 \cdot 13 \cdot 37$$$.

The prime factorization is $$$1443 = 3 \cdot 13 \cdot 37$$$A.