# Prime factorization of $260$

The calculator will find the prime factorization of $260$, 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 $260$.

### Solution

Start with the number $2$.

Determine whether $260$ is divisible by $2$.

It is divisible, thus, divide $260$ by ${\color{green}2}$: $\frac{260}{2} = {\color{red}130}$.

Determine whether $130$ is divisible by $2$.

It is divisible, thus, divide $130$ by ${\color{green}2}$: $\frac{130}{2} = {\color{red}65}$.

Determine whether $65$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $65$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $65$ is divisible by $5$.

It is divisible, thus, divide $65$ by ${\color{green}5}$: $\frac{65}{5} = {\color{red}13}$.

The prime number ${\color{green}13}$ has no other factors then $1$ and ${\color{green}13}$: $\frac{13}{13} = {\color{red}1}$.

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: $260 = 2^{2} \cdot 5 \cdot 13$.

The prime factorization is $260 = 2^{2} \cdot 5 \cdot 13$A.