Prime factorization of $$$2009$$$

Find the prime factorization of $$$2009$$$.

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

Determine whether $$$2009$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2009$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$2009$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$2009$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$2009$$$ by $$${\color{green}7}$$$: $$$\frac{2009}{7} = {\color{red}287}$$$.

Determine whether $$$287$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$287$$$ by $$${\color{green}7}$$$: $$$\frac{287}{7} = {\color{red}41}$$$.

The prime number $$${\color{green}41}$$$ has no other factors then $$$1$$$ and $$${\color{green}41}$$$: $$$\frac{41}{41} = {\color{red}1}$$$.

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: $$$2009 = 7^{2} \cdot 41$$$.

The prime factorization is $$$2009 = 7^{2} \cdot 41$$$A.