# Prime factorization of $1309$

The calculator will find the prime factorization of $1309$, with steps shown.

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Find the prime factorization of $1309$.

### Solution

Start with the number $2$.

Determine whether $1309$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1309$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $1309$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $1309$ is divisible by $7$.

It is divisible, thus, divide $1309$ by ${\color{green}7}$: $\frac{1309}{7} = {\color{red}187}$.

Determine whether $187$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $187$ is divisible by $11$.

It is divisible, thus, divide $187$ by ${\color{green}11}$: $\frac{187}{11} = {\color{red}17}$.

The prime number ${\color{green}17}$ has no other factors then $1$ and ${\color{green}17}$: $\frac{17}{17} = {\color{red}1}$.

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: $1309 = 7 \cdot 11 \cdot 17$.

The prime factorization is $1309 = 7 \cdot 11 \cdot 17$A.