Prime factorization of $$$4041$$$

Find the prime factorization of $$$4041$$$.

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

Determine whether $$$4041$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$4041$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$4041$$$ by $$${\color{green}3}$$$: $$$\frac{4041}{3} = {\color{red}1347}$$$.

Determine whether $$$1347$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1347$$$ by $$${\color{green}3}$$$: $$$\frac{1347}{3} = {\color{red}449}$$$.

The prime number $$${\color{green}449}$$$ has no other factors then $$$1$$$ and $$${\color{green}449}$$$: $$$\frac{449}{449} = {\color{red}1}$$$.

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: $$$4041 = 3^{2} \cdot 449$$$.

The prime factorization is $$$4041 = 3^{2} \cdot 449$$$A.