Prime factorization of $$$4122$$$

Find the prime factorization of $$$4122$$$.

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

Determine whether $$$4122$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4122$$$ by $$${\color{green}2}$$$: $$$\frac{4122}{2} = {\color{red}2061}$$$.

Determine whether $$$2061$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2061$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$2061$$$ by $$${\color{green}3}$$$: $$$\frac{2061}{3} = {\color{red}687}$$$.

Determine whether $$$687$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$687$$$ by $$${\color{green}3}$$$: $$$\frac{687}{3} = {\color{red}229}$$$.

The prime number $$${\color{green}229}$$$ has no other factors then $$$1$$$ and $$${\color{green}229}$$$: $$$\frac{229}{229} = {\color{red}1}$$$.

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: $$$4122 = 2 \cdot 3^{2} \cdot 229$$$.

The prime factorization is $$$4122 = 2 \cdot 3^{2} \cdot 229$$$A.