Prime factorization of $$$2168$$$

Find the prime factorization of $$$2168$$$.

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

Determine whether $$$2168$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2168$$$ by $$${\color{green}2}$$$: $$$\frac{2168}{2} = {\color{red}1084}$$$.

Determine whether $$$1084$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1084$$$ by $$${\color{green}2}$$$: $$$\frac{1084}{2} = {\color{red}542}$$$.

Determine whether $$$542$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$542$$$ by $$${\color{green}2}$$$: $$$\frac{542}{2} = {\color{red}271}$$$.

The prime number $$${\color{green}271}$$$ has no other factors then $$$1$$$ and $$${\color{green}271}$$$: $$$\frac{271}{271} = {\color{red}1}$$$.

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: $$$2168 = 2^{3} \cdot 271$$$.

The prime factorization is $$$2168 = 2^{3} \cdot 271$$$A.