Prime factorization of $$$3816$$$

Find the prime factorization of $$$3816$$$.

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

Determine whether $$$3816$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3816$$$ by $$${\color{green}2}$$$: $$$\frac{3816}{2} = {\color{red}1908}$$$.

Determine whether $$$1908$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1908$$$ by $$${\color{green}2}$$$: $$$\frac{1908}{2} = {\color{red}954}$$$.

Determine whether $$$954$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$954$$$ by $$${\color{green}2}$$$: $$$\frac{954}{2} = {\color{red}477}$$$.

Determine whether $$$477$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$477$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$477$$$ by $$${\color{green}3}$$$: $$$\frac{477}{3} = {\color{red}159}$$$.

Determine whether $$$159$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$159$$$ by $$${\color{green}3}$$$: $$$\frac{159}{3} = {\color{red}53}$$$.

The prime number $$${\color{green}53}$$$ has no other factors then $$$1$$$ and $$${\color{green}53}$$$: $$$\frac{53}{53} = {\color{red}1}$$$.

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: $$$3816 = 2^{3} \cdot 3^{2} \cdot 53$$$.

The prime factorization is $$$3816 = 2^{3} \cdot 3^{2} \cdot 53$$$A.