Prime factorization of $$$2511$$$

Find the prime factorization of $$$2511$$$.

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

Determine whether $$$2511$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2511$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$2511$$$ by $$${\color{green}3}$$$: $$$\frac{2511}{3} = {\color{red}837}$$$.

Determine whether $$$837$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$837$$$ by $$${\color{green}3}$$$: $$$\frac{837}{3} = {\color{red}279}$$$.

Determine whether $$$279$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$279$$$ by $$${\color{green}3}$$$: $$$\frac{279}{3} = {\color{red}93}$$$.

Determine whether $$$93$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$93$$$ by $$${\color{green}3}$$$: $$$\frac{93}{3} = {\color{red}31}$$$.

The prime number $$${\color{green}31}$$$ has no other factors then $$$1$$$ and $$${\color{green}31}$$$: $$$\frac{31}{31} = {\color{red}1}$$$.

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: $$$2511 = 3^{4} \cdot 31$$$.

The prime factorization is $$$2511 = 3^{4} \cdot 31$$$A.