Prime factorization of $$$1903$$$

Find the prime factorization of $$$1903$$$.

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

Determine whether $$$1903$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1903$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1903$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$1903$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$1903$$$ is divisible by $$$11$$$.

It is divisible, thus, divide $$$1903$$$ by $$${\color{green}11}$$$: $$$\frac{1903}{11} = {\color{red}173}$$$.

The prime number $$${\color{green}173}$$$ has no other factors then $$$1$$$ and $$${\color{green}173}$$$: $$$\frac{173}{173} = {\color{red}1}$$$.

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: $$$1903 = 11 \cdot 173$$$.

The prime factorization is $$$1903 = 11 \cdot 173$$$A.