Prime factorization of $$$3768$$$

Find the prime factorization of $$$3768$$$.

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

Determine whether $$$3768$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3768$$$ by $$${\color{green}2}$$$: $$$\frac{3768}{2} = {\color{red}1884}$$$.

Determine whether $$$1884$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1884$$$ by $$${\color{green}2}$$$: $$$\frac{1884}{2} = {\color{red}942}$$$.

Determine whether $$$942$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$942$$$ by $$${\color{green}2}$$$: $$$\frac{942}{2} = {\color{red}471}$$$.

Determine whether $$$471$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$471$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$471$$$ by $$${\color{green}3}$$$: $$$\frac{471}{3} = {\color{red}157}$$$.

The prime number $$${\color{green}157}$$$ has no other factors then $$$1$$$ and $$${\color{green}157}$$$: $$$\frac{157}{157} = {\color{red}1}$$$.

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: $$$3768 = 2^{3} \cdot 3 \cdot 157$$$.

The prime factorization is $$$3768 = 2^{3} \cdot 3 \cdot 157$$$A.