Prime factorization of $$$3690$$$

Find the prime factorization of $$$3690$$$.

Start with the number $$$2$$$.

Determine whether $$$3690$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3690$$$ by $$${\color{green}2}$$$: $$$\frac{3690}{2} = {\color{red}1845}$$$.

Determine whether $$$1845$$$ is divisible by $$$2$$$.

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

The next prime number is $$$3$$$.

Determine whether $$$1845$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1845$$$ by $$${\color{green}3}$$$: $$$\frac{1845}{3} = {\color{red}615}$$$.

Determine whether $$$615$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$615$$$ by $$${\color{green}3}$$$: $$$\frac{615}{3} = {\color{red}205}$$$.

Determine whether $$$205$$$ is divisible by $$$3$$$.

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

The next prime number is $$$5$$$.

Determine whether $$$205$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$205$$$ by $$${\color{green}5}$$$: $$$\frac{205}{5} = {\color{red}41}$$$.

The prime number $$${\color{green}41}$$$ has no other factors then $$$1$$$ and $$${\color{green}41}$$$: $$$\frac{41}{41} = {\color{red}1}$$$.

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: $$$3690 = 2 \cdot 3^{2} \cdot 5 \cdot 41$$$.

The prime factorization is $$$3690 = 2 \cdot 3^{2} \cdot 5 \cdot 41$$$A.