Prime factorization of $$$3904$$$

Find the prime factorization of $$$3904$$$.

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

Determine whether $$$3904$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3904$$$ by $$${\color{green}2}$$$: $$$\frac{3904}{2} = {\color{red}1952}$$$.

Determine whether $$$1952$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1952$$$ by $$${\color{green}2}$$$: $$$\frac{1952}{2} = {\color{red}976}$$$.

Determine whether $$$976$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$976$$$ by $$${\color{green}2}$$$: $$$\frac{976}{2} = {\color{red}488}$$$.

Determine whether $$$488$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$488$$$ by $$${\color{green}2}$$$: $$$\frac{488}{2} = {\color{red}244}$$$.

Determine whether $$$244$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$244$$$ by $$${\color{green}2}$$$: $$$\frac{244}{2} = {\color{red}122}$$$.

Determine whether $$$122$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$122$$$ by $$${\color{green}2}$$$: $$$\frac{122}{2} = {\color{red}61}$$$.

The prime number $$${\color{green}61}$$$ has no other factors then $$$1$$$ and $$${\color{green}61}$$$: $$$\frac{61}{61} = {\color{red}1}$$$.

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: $$$3904 = 2^{6} \cdot 61$$$.

The prime factorization is $$$3904 = 2^{6} \cdot 61$$$A.