Prime factorization of $$$1616$$$

Find the prime factorization of $$$1616$$$.

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

Determine whether $$$1616$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1616$$$ by $$${\color{green}2}$$$: $$$\frac{1616}{2} = {\color{red}808}$$$.

Determine whether $$$808$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$808$$$ by $$${\color{green}2}$$$: $$$\frac{808}{2} = {\color{red}404}$$$.

Determine whether $$$404$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$404$$$ by $$${\color{green}2}$$$: $$$\frac{404}{2} = {\color{red}202}$$$.

Determine whether $$$202$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$202$$$ by $$${\color{green}2}$$$: $$$\frac{202}{2} = {\color{red}101}$$$.

The prime number $$${\color{green}101}$$$ has no other factors then $$$1$$$ and $$${\color{green}101}$$$: $$$\frac{101}{101} = {\color{red}1}$$$.

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: $$$1616 = 2^{4} \cdot 101$$$.

The prime factorization is $$$1616 = 2^{4} \cdot 101$$$A.