# Prime factorization of $3609$

The calculator will find the prime factorization of $3609$, with steps shown.

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Find the prime factorization of $3609$.

### Solution

Start with the number $2$.

Determine whether $3609$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $3609$ is divisible by $3$.

It is divisible, thus, divide $3609$ by ${\color{green}3}$: $\frac{3609}{3} = {\color{red}1203}$.

Determine whether $1203$ is divisible by $3$.

It is divisible, thus, divide $1203$ by ${\color{green}3}$: $\frac{1203}{3} = {\color{red}401}$.

The prime number ${\color{green}401}$ has no other factors then $1$ and ${\color{green}401}$: $\frac{401}{401} = {\color{red}1}$.

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: $3609 = 3^{2} \cdot 401$.

The prime factorization is $3609 = 3^{2} \cdot 401$A.