Prime factorization of $$$4065$$$

Find the prime factorization of $$$4065$$$.

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

Determine whether $$$4065$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$4065$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$4065$$$ by $$${\color{green}3}$$$: $$$\frac{4065}{3} = {\color{red}1355}$$$.

Determine whether $$$1355$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1355$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$1355$$$ by $$${\color{green}5}$$$: $$$\frac{1355}{5} = {\color{red}271}$$$.

The prime number $$${\color{green}271}$$$ has no other factors then $$$1$$$ and $$${\color{green}271}$$$: $$$\frac{271}{271} = {\color{red}1}$$$.

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: $$$4065 = 3 \cdot 5 \cdot 271$$$.

The prime factorization is $$$4065 = 3 \cdot 5 \cdot 271$$$A.