Prime factorization of $$$3409$$$

Find the prime factorization of $$$3409$$$.

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

Determine whether $$$3409$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$3409$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$3409$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$3409$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$3409$$$ by $$${\color{green}7}$$$: $$$\frac{3409}{7} = {\color{red}487}$$$.

The prime number $$${\color{green}487}$$$ has no other factors then $$$1$$$ and $$${\color{green}487}$$$: $$$\frac{487}{487} = {\color{red}1}$$$.

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: $$$3409 = 7 \cdot 487$$$.

The prime factorization is $$$3409 = 7 \cdot 487$$$A.