# Prime factorization of $3105$

The calculator will find the prime factorization of $3105$, with steps shown.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Find the prime factorization of $3105$.

### Solution

Start with the number $2$.

Determine whether $3105$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $3105$ is divisible by $3$.

It is divisible, thus, divide $3105$ by ${\color{green}3}$: $\frac{3105}{3} = {\color{red}1035}$.

Determine whether $1035$ is divisible by $3$.

It is divisible, thus, divide $1035$ by ${\color{green}3}$: $\frac{1035}{3} = {\color{red}345}$.

Determine whether $345$ is divisible by $3$.

It is divisible, thus, divide $345$ by ${\color{green}3}$: $\frac{345}{3} = {\color{red}115}$.

Determine whether $115$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $115$ is divisible by $5$.

It is divisible, thus, divide $115$ by ${\color{green}5}$: $\frac{115}{5} = {\color{red}23}$.

The prime number ${\color{green}23}$ has no other factors then $1$ and ${\color{green}23}$: $\frac{23}{23} = {\color{red}1}$.

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: $3105 = 3^{3} \cdot 5 \cdot 23$.

The prime factorization is $3105 = 3^{3} \cdot 5 \cdot 23$A.