Prime factorization of $$$4095$$$

Find the prime factorization of $$$4095$$$.

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

Determine whether $$$4095$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$4095$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$4095$$$ by $$${\color{green}3}$$$: $$$\frac{4095}{3} = {\color{red}1365}$$$.

Determine whether $$$1365$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1365$$$ by $$${\color{green}3}$$$: $$$\frac{1365}{3} = {\color{red}455}$$$.

Determine whether $$$455$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$455$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$455$$$ by $$${\color{green}5}$$$: $$$\frac{455}{5} = {\color{red}91}$$$.

Determine whether $$$91$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$91$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$91$$$ by $$${\color{green}7}$$$: $$$\frac{91}{7} = {\color{red}13}$$$.

The prime number $$${\color{green}13}$$$ has no other factors then $$$1$$$ and $$${\color{green}13}$$$: $$$\frac{13}{13} = {\color{red}1}$$$.

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: $$$4095 = 3^{2} \cdot 5 \cdot 7 \cdot 13$$$.

The prime factorization is $$$4095 = 3^{2} \cdot 5 \cdot 7 \cdot 13$$$A.