Prime factorization of $$$4401$$$

Find the prime factorization of $$$4401$$$.

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

Determine whether $$$4401$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$4401$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$4401$$$ by $$${\color{green}3}$$$: $$$\frac{4401}{3} = {\color{red}1467}$$$.

Determine whether $$$1467$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1467$$$ by $$${\color{green}3}$$$: $$$\frac{1467}{3} = {\color{red}489}$$$.

Determine whether $$$489$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$489$$$ by $$${\color{green}3}$$$: $$$\frac{489}{3} = {\color{red}163}$$$.

The prime number $$${\color{green}163}$$$ has no other factors then $$$1$$$ and $$${\color{green}163}$$$: $$$\frac{163}{163} = {\color{red}1}$$$.

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: $$$4401 = 3^{3} \cdot 163$$$.

The prime factorization is $$$4401 = 3^{3} \cdot 163$$$A.