Prime factorization of $$$3285$$$

Find the prime factorization of $$$3285$$$.

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

Determine whether $$$3285$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$3285$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$3285$$$ by $$${\color{green}3}$$$: $$$\frac{3285}{3} = {\color{red}1095}$$$.

Determine whether $$$1095$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1095$$$ by $$${\color{green}3}$$$: $$$\frac{1095}{3} = {\color{red}365}$$$.

Determine whether $$$365$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$365$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$365$$$ by $$${\color{green}5}$$$: $$$\frac{365}{5} = {\color{red}73}$$$.

The prime number $$${\color{green}73}$$$ has no other factors then $$$1$$$ and $$${\color{green}73}$$$: $$$\frac{73}{73} = {\color{red}1}$$$.

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: $$$3285 = 3^{2} \cdot 5 \cdot 73$$$.

The prime factorization is $$$3285 = 3^{2} \cdot 5 \cdot 73$$$A.