Prime factorization of $$$2728$$$

Find the prime factorization of $$$2728$$$.

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

Determine whether $$$2728$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2728$$$ by $$${\color{green}2}$$$: $$$\frac{2728}{2} = {\color{red}1364}$$$.

Determine whether $$$1364$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1364$$$ by $$${\color{green}2}$$$: $$$\frac{1364}{2} = {\color{red}682}$$$.

Determine whether $$$682$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$682$$$ by $$${\color{green}2}$$$: $$$\frac{682}{2} = {\color{red}341}$$$.

Determine whether $$$341$$$ is divisible by $$$2$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$3$$$.

Determine whether $$$341$$$ is divisible by $$$3$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$5$$$.

Determine whether $$$341$$$ is divisible by $$$5$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$7$$$.

Determine whether $$$341$$$ is divisible by $$$7$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$11$$$.

Determine whether $$$341$$$ is divisible by $$$11$$$.

It is divisible, thus, divide $$$341$$$ by $$${\color{green}11}$$$: $$$\frac{341}{11} = {\color{red}31}$$$.

The prime number $$${\color{green}31}$$$ has no other factors then $$$1$$$ and $$${\color{green}31}$$$: $$$\frac{31}{31} = {\color{red}1}$$$.

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: $$$2728 = 2^{3} \cdot 11 \cdot 31$$$.

The prime factorization is $$$2728 = 2^{3} \cdot 11 \cdot 31$$$A.