Prime factorization of $$$3864$$$

Find the prime factorization of $$$3864$$$.

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

Determine whether $$$3864$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3864$$$ by $$${\color{green}2}$$$: $$$\frac{3864}{2} = {\color{red}1932}$$$.

Determine whether $$$1932$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1932$$$ by $$${\color{green}2}$$$: $$$\frac{1932}{2} = {\color{red}966}$$$.

Determine whether $$$966$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$966$$$ by $$${\color{green}2}$$$: $$$\frac{966}{2} = {\color{red}483}$$$.

Determine whether $$$483$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$483$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$483$$$ by $$${\color{green}3}$$$: $$$\frac{483}{3} = {\color{red}161}$$$.

Determine whether $$$161$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$161$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$161$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$161$$$ by $$${\color{green}7}$$$: $$$\frac{161}{7} = {\color{red}23}$$$.

The prime number $$${\color{green}23}$$$ has no other factors then $$$1$$$ and $$${\color{green}23}$$$: $$$\frac{23}{23} = {\color{red}1}$$$.

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: $$$3864 = 2^{3} \cdot 3 \cdot 7 \cdot 23$$$.

The prime factorization is $$$3864 = 2^{3} \cdot 3 \cdot 7 \cdot 23$$$A.