Prime factorization of $$$2163$$$

Find the prime factorization of $$$2163$$$.

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

Determine whether $$$2163$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2163$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$2163$$$ by $$${\color{green}3}$$$: $$$\frac{2163}{3} = {\color{red}721}$$$.

Determine whether $$$721$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$721$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$721$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$721$$$ by $$${\color{green}7}$$$: $$$\frac{721}{7} = {\color{red}103}$$$.

The prime number $$${\color{green}103}$$$ has no other factors then $$$1$$$ and $$${\color{green}103}$$$: $$$\frac{103}{103} = {\color{red}1}$$$.

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: $$$2163 = 3 \cdot 7 \cdot 103$$$.

The prime factorization is $$$2163 = 3 \cdot 7 \cdot 103$$$A.