Prime factorization of $$$4167$$$

Find the prime factorization of $$$4167$$$.

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

Determine whether $$$4167$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$4167$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$4167$$$ by $$${\color{green}3}$$$: $$$\frac{4167}{3} = {\color{red}1389}$$$.

Determine whether $$$1389$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1389$$$ by $$${\color{green}3}$$$: $$$\frac{1389}{3} = {\color{red}463}$$$.

The prime number $$${\color{green}463}$$$ has no other factors then $$$1$$$ and $$${\color{green}463}$$$: $$$\frac{463}{463} = {\color{red}1}$$$.

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: $$$4167 = 3^{2} \cdot 463$$$.

The prime factorization is $$$4167 = 3^{2} \cdot 463$$$A.