Prime factorization of $$$2152$$$

Find the prime factorization of $$$2152$$$.

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

Determine whether $$$2152$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2152$$$ by $$${\color{green}2}$$$: $$$\frac{2152}{2} = {\color{red}1076}$$$.

Determine whether $$$1076$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1076$$$ by $$${\color{green}2}$$$: $$$\frac{1076}{2} = {\color{red}538}$$$.

Determine whether $$$538$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$538$$$ by $$${\color{green}2}$$$: $$$\frac{538}{2} = {\color{red}269}$$$.

The prime number $$${\color{green}269}$$$ has no other factors then $$$1$$$ and $$${\color{green}269}$$$: $$$\frac{269}{269} = {\color{red}1}$$$.

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: $$$2152 = 2^{3} \cdot 269$$$.

The prime factorization is $$$2152 = 2^{3} \cdot 269$$$A.