Prime factorization of $$$3546$$$

Find the prime factorization of $$$3546$$$.

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

Determine whether $$$3546$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3546$$$ by $$${\color{green}2}$$$: $$$\frac{3546}{2} = {\color{red}1773}$$$.

Determine whether $$$1773$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1773$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1773$$$ by $$${\color{green}3}$$$: $$$\frac{1773}{3} = {\color{red}591}$$$.

Determine whether $$$591$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$591$$$ by $$${\color{green}3}$$$: $$$\frac{591}{3} = {\color{red}197}$$$.

The prime number $$${\color{green}197}$$$ has no other factors then $$$1$$$ and $$${\color{green}197}$$$: $$$\frac{197}{197} = {\color{red}1}$$$.

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: $$$3546 = 2 \cdot 3^{2} \cdot 197$$$.

The prime factorization is $$$3546 = 2 \cdot 3^{2} \cdot 197$$$A.