Prime factorization of $$$2409$$$

Find the prime factorization of $$$2409$$$.

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

Determine whether $$$2409$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2409$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$2409$$$ by $$${\color{green}3}$$$: $$$\frac{2409}{3} = {\color{red}803}$$$.

Determine whether $$$803$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$803$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$803$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$803$$$ is divisible by $$$11$$$.

It is divisible, thus, divide $$$803$$$ by $$${\color{green}11}$$$: $$$\frac{803}{11} = {\color{red}73}$$$.

The prime number $$${\color{green}73}$$$ has no other factors then $$$1$$$ and $$${\color{green}73}$$$: $$$\frac{73}{73} = {\color{red}1}$$$.

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: $$$2409 = 3 \cdot 11 \cdot 73$$$.

The prime factorization is $$$2409 = 3 \cdot 11 \cdot 73$$$A.