# Prime factorization of $3913$

The calculator will find the prime factorization of $3913$, 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 $3913$.

### Solution

Start with the number $2$.

Determine whether $3913$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $3913$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $3913$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $3913$ is divisible by $7$.

It is divisible, thus, divide $3913$ by ${\color{green}7}$: $\frac{3913}{7} = {\color{red}559}$.

Determine whether $559$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $559$ is divisible by $11$.

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

The next prime number is $13$.

Determine whether $559$ is divisible by $13$.

It is divisible, thus, divide $559$ by ${\color{green}13}$: $\frac{559}{13} = {\color{red}43}$.

The prime number ${\color{green}43}$ has no other factors then $1$ and ${\color{green}43}$: $\frac{43}{43} = {\color{red}1}$.

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: $3913 = 7 \cdot 13 \cdot 43$.

The prime factorization is $3913 = 7 \cdot 13 \cdot 43$A.