Prime factorization of $$$1696$$$

Find the prime factorization of $$$1696$$$.

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

Determine whether $$$1696$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1696$$$ by $$${\color{green}2}$$$: $$$\frac{1696}{2} = {\color{red}848}$$$.

Determine whether $$$848$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$848$$$ by $$${\color{green}2}$$$: $$$\frac{848}{2} = {\color{red}424}$$$.

Determine whether $$$424$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$424$$$ by $$${\color{green}2}$$$: $$$\frac{424}{2} = {\color{red}212}$$$.

Determine whether $$$212$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$212$$$ by $$${\color{green}2}$$$: $$$\frac{212}{2} = {\color{red}106}$$$.

Determine whether $$$106$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$106$$$ by $$${\color{green}2}$$$: $$$\frac{106}{2} = {\color{red}53}$$$.

The prime number $$${\color{green}53}$$$ has no other factors then $$$1$$$ and $$${\color{green}53}$$$: $$$\frac{53}{53} = {\color{red}1}$$$.

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: $$$1696 = 2^{5} \cdot 53$$$.

The prime factorization is $$$1696 = 2^{5} \cdot 53$$$A.