# Prime factorization of $2409$

The calculator will find the prime factorization of $2409$, with steps shown.

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Find the prime factorization of $2409$.

### Solution

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.