Prime factorization of $$$4995$$$

Find the prime factorization of $$$4995$$$.

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

Determine whether $$$4995$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$4995$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$4995$$$ by $$${\color{green}3}$$$: $$$\frac{4995}{3} = {\color{red}1665}$$$.

Determine whether $$$1665$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1665$$$ by $$${\color{green}3}$$$: $$$\frac{1665}{3} = {\color{red}555}$$$.

Determine whether $$$555$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$555$$$ by $$${\color{green}3}$$$: $$$\frac{555}{3} = {\color{red}185}$$$.

Determine whether $$$185$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$185$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$185$$$ by $$${\color{green}5}$$$: $$$\frac{185}{5} = {\color{red}37}$$$.

The prime number $$${\color{green}37}$$$ has no other factors then $$$1$$$ and $$${\color{green}37}$$$: $$$\frac{37}{37} = {\color{red}1}$$$.

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: $$$4995 = 3^{3} \cdot 5 \cdot 37$$$.

The prime factorization is $$$4995 = 3^{3} \cdot 5 \cdot 37$$$A.