# Prime factorization of $2511$

The calculator will find the prime factorization of $2511$, with steps shown.

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Find the prime factorization of $2511$.

### Solution

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.