Prime factorization of $$$728$$$

Find the prime factorization of $$$728$$$.

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

Determine whether $$$728$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$728$$$ by $$${\color{green}2}$$$: $$$\frac{728}{2} = {\color{red}364}$$$.

Determine whether $$$364$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$364$$$ by $$${\color{green}2}$$$: $$$\frac{364}{2} = {\color{red}182}$$$.

Determine whether $$$182$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$182$$$ by $$${\color{green}2}$$$: $$$\frac{182}{2} = {\color{red}91}$$$.

Determine whether $$$91$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$91$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$91$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$91$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$91$$$ by $$${\color{green}7}$$$: $$$\frac{91}{7} = {\color{red}13}$$$.

The prime number $$${\color{green}13}$$$ has no other factors then $$$1$$$ and $$${\color{green}13}$$$: $$$\frac{13}{13} = {\color{red}1}$$$.

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: $$$728 = 2^{3} \cdot 7 \cdot 13$$$.

The prime factorization is $$$728 = 2^{3} \cdot 7 \cdot 13$$$A.