Prime factorization of $$$2176$$$

Find the prime factorization of $$$2176$$$.

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

Determine whether $$$2176$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2176$$$ by $$${\color{green}2}$$$: $$$\frac{2176}{2} = {\color{red}1088}$$$.

Determine whether $$$1088$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1088$$$ by $$${\color{green}2}$$$: $$$\frac{1088}{2} = {\color{red}544}$$$.

Determine whether $$$544$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$544$$$ by $$${\color{green}2}$$$: $$$\frac{544}{2} = {\color{red}272}$$$.

Determine whether $$$272$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$272$$$ by $$${\color{green}2}$$$: $$$\frac{272}{2} = {\color{red}136}$$$.

Determine whether $$$136$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$136$$$ by $$${\color{green}2}$$$: $$$\frac{136}{2} = {\color{red}68}$$$.

Determine whether $$$68$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$68$$$ by $$${\color{green}2}$$$: $$$\frac{68}{2} = {\color{red}34}$$$.

Determine whether $$$34$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$34$$$ by $$${\color{green}2}$$$: $$$\frac{34}{2} = {\color{red}17}$$$.

The prime number $$${\color{green}17}$$$ has no other factors then $$$1$$$ and $$${\color{green}17}$$$: $$$\frac{17}{17} = {\color{red}1}$$$.

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: $$$2176 = 2^{7} \cdot 17$$$.

The prime factorization is $$$2176 = 2^{7} \cdot 17$$$A.