# Prime factorization of $3606$

The calculator will find the prime factorization of $3606$, with steps shown.

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Find the prime factorization of $3606$.

### Solution

Start with the number $2$.

Determine whether $3606$ is divisible by $2$.

It is divisible, thus, divide $3606$ by ${\color{green}2}$: $\frac{3606}{2} = {\color{red}1803}$.

Determine whether $1803$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1803$ is divisible by $3$.

It is divisible, thus, divide $1803$ by ${\color{green}3}$: $\frac{1803}{3} = {\color{red}601}$.

The prime number ${\color{green}601}$ has no other factors then $1$ and ${\color{green}601}$: $\frac{601}{601} = {\color{red}1}$.

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: $3606 = 2 \cdot 3 \cdot 601$.

The prime factorization is $3606 = 2 \cdot 3 \cdot 601$A.