Prime factorization of $$$1819$$$

Find the prime factorization of $$$1819$$$.

Start with the number $$$2$$$.

Determine whether $$$1819$$$ is divisible by $$$2$$$.

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

The next prime number is $$$3$$$.

Determine whether $$$1819$$$ is divisible by $$$3$$$.

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

The next prime number is $$$5$$$.

Determine whether $$$1819$$$ is divisible by $$$5$$$.

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

The next prime number is $$$7$$$.

Determine whether $$$1819$$$ is divisible by $$$7$$$.

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

The next prime number is $$$11$$$.

Determine whether $$$1819$$$ is divisible by $$$11$$$.

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

The next prime number is $$$13$$$.

Determine whether $$$1819$$$ is divisible by $$$13$$$.

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

The next prime number is $$$17$$$.

Determine whether $$$1819$$$ is divisible by $$$17$$$.

It is divisible, thus, divide $$$1819$$$ by $$${\color{green}17}$$$: $$$\frac{1819}{17} = {\color{red}107}$$$.

The prime number $$${\color{green}107}$$$ has no other factors then $$$1$$$ and $$${\color{green}107}$$$: $$$\frac{107}{107} = {\color{red}1}$$$.

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: $$$1819 = 17 \cdot 107$$$.

The prime factorization is $$$1819 = 17 \cdot 107$$$A.