Prime factorization of $$$2169$$$

Find the prime factorization of $$$2169$$$.

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

Determine whether $$$2169$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2169$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$2169$$$ by $$${\color{green}3}$$$: $$$\frac{2169}{3} = {\color{red}723}$$$.

Determine whether $$$723$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$723$$$ by $$${\color{green}3}$$$: $$$\frac{723}{3} = {\color{red}241}$$$.

The prime number $$${\color{green}241}$$$ has no other factors then $$$1$$$ and $$${\color{green}241}$$$: $$$\frac{241}{241} = {\color{red}1}$$$.

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: $$$2169 = 3^{2} \cdot 241$$$.

The prime factorization is $$$2169 = 3^{2} \cdot 241$$$A.