Prime factorization of $$$3728$$$

Find the prime factorization of $$$3728$$$.

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

Determine whether $$$3728$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3728$$$ by $$${\color{green}2}$$$: $$$\frac{3728}{2} = {\color{red}1864}$$$.

Determine whether $$$1864$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1864$$$ by $$${\color{green}2}$$$: $$$\frac{1864}{2} = {\color{red}932}$$$.

Determine whether $$$932$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$932$$$ by $$${\color{green}2}$$$: $$$\frac{932}{2} = {\color{red}466}$$$.

Determine whether $$$466$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$466$$$ by $$${\color{green}2}$$$: $$$\frac{466}{2} = {\color{red}233}$$$.

The prime number $$${\color{green}233}$$$ has no other factors then $$$1$$$ and $$${\color{green}233}$$$: $$$\frac{233}{233} = {\color{red}1}$$$.

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: $$$3728 = 2^{4} \cdot 233$$$.

The prime factorization is $$$3728 = 2^{4} \cdot 233$$$A.