# Prime factorization of $3582$

The calculator will find the prime factorization of $3582$, with steps shown.

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Find the prime factorization of $3582$.

### Solution

Start with the number $2$.

Determine whether $3582$ is divisible by $2$.

It is divisible, thus, divide $3582$ by ${\color{green}2}$: $\frac{3582}{2} = {\color{red}1791}$.

Determine whether $1791$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1791$ is divisible by $3$.

It is divisible, thus, divide $1791$ by ${\color{green}3}$: $\frac{1791}{3} = {\color{red}597}$.

Determine whether $597$ is divisible by $3$.

It is divisible, thus, divide $597$ by ${\color{green}3}$: $\frac{597}{3} = {\color{red}199}$.

The prime number ${\color{green}199}$ has no other factors then $1$ and ${\color{green}199}$: $\frac{199}{199} = {\color{red}1}$.

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: $3582 = 2 \cdot 3^{2} \cdot 199$.

The prime factorization is $3582 = 2 \cdot 3^{2} \cdot 199$A.