Prime factorization of $$$4116$$$

Find the prime factorization of $$$4116$$$.

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

Determine whether $$$4116$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4116$$$ by $$${\color{green}2}$$$: $$$\frac{4116}{2} = {\color{red}2058}$$$.

Determine whether $$$2058$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2058$$$ by $$${\color{green}2}$$$: $$$\frac{2058}{2} = {\color{red}1029}$$$.

Determine whether $$$1029$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1029$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1029$$$ by $$${\color{green}3}$$$: $$$\frac{1029}{3} = {\color{red}343}$$$.

Determine whether $$$343$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$343$$$ is divisible by $$$5$$$.

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

The next prime number is $$$7$$$.

Determine whether $$$343$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$343$$$ by $$${\color{green}7}$$$: $$$\frac{343}{7} = {\color{red}49}$$$.

Determine whether $$$49$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$49$$$ by $$${\color{green}7}$$$: $$$\frac{49}{7} = {\color{red}7}$$$.

The prime number $$${\color{green}7}$$$ has no other factors then $$$1$$$ and $$${\color{green}7}$$$: $$$\frac{7}{7} = {\color{red}1}$$$.

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: $$$4116 = 2^{2} \cdot 3 \cdot 7^{3}$$$.

The prime factorization is $$$4116 = 2^{2} \cdot 3 \cdot 7^{3}$$$A.