# Prime factorization of $3409$

The calculator will find the prime factorization of $3409$, with steps shown.

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Find the prime factorization of $3409$.

### Solution

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.