Prime factorization of $$$3582$$$

Find the prime factorization of $$$3582$$$.

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.