Prime factorization of $$$2985$$$

Find the prime factorization of $$$2985$$$.

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

Determine whether $$$2985$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2985$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$2985$$$ by $$${\color{green}3}$$$: $$$\frac{2985}{3} = {\color{red}995}$$$.

Determine whether $$$995$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$995$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$995$$$ by $$${\color{green}5}$$$: $$$\frac{995}{5} = {\color{red}199}$$$.

The prime number $$${\color{green}199}$$$ has no other factors then $$$1$$$ and $$${\color{green}199}$$$: $$$\frac{199}{199} = {\color{red}1}$$$.

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: $$$2985 = 3 \cdot 5 \cdot 199$$$.

The prime factorization is $$$2985 = 3 \cdot 5 \cdot 199$$$A.