Prime factorization of $$$1309$$$

Find the prime factorization of $$$1309$$$.

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.