Prime factorization of $$$2872$$$

Find the prime factorization of $$$2872$$$.

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

Determine whether $$$2872$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2872$$$ by $$${\color{green}2}$$$: $$$\frac{2872}{2} = {\color{red}1436}$$$.

Determine whether $$$1436$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1436$$$ by $$${\color{green}2}$$$: $$$\frac{1436}{2} = {\color{red}718}$$$.

Determine whether $$$718$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$718$$$ by $$${\color{green}2}$$$: $$$\frac{718}{2} = {\color{red}359}$$$.

The prime number $$${\color{green}359}$$$ has no other factors then $$$1$$$ and $$${\color{green}359}$$$: $$$\frac{359}{359} = {\color{red}1}$$$.

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: $$$2872 = 2^{3} \cdot 359$$$.

The prime factorization is $$$2872 = 2^{3} \cdot 359$$$A.