# Prime factorization of $3515$

The calculator will find the prime factorization of $3515$, 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 $3515$.

### Solution

Start with the number $2$.

Determine whether $3515$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $3515$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $3515$ is divisible by $5$.

It is divisible, thus, divide $3515$ by ${\color{green}5}$: $\frac{3515}{5} = {\color{red}703}$.

Determine whether $703$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $703$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $703$ is divisible by $11$.

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

The next prime number is $13$.

Determine whether $703$ is divisible by $13$.

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

The next prime number is $17$.

Determine whether $703$ is divisible by $17$.

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

The next prime number is $19$.

Determine whether $703$ is divisible by $19$.

It is divisible, thus, divide $703$ by ${\color{green}19}$: $\frac{703}{19} = {\color{red}37}$.

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: $3515 = 5 \cdot 19 \cdot 37$.

The prime factorization is $3515 = 5 \cdot 19 \cdot 37$A.