Prime factorization of $$$3200$$$

Find the prime factorization of $$$3200$$$.

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

Determine whether $$$3200$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3200$$$ by $$${\color{green}2}$$$: $$$\frac{3200}{2} = {\color{red}1600}$$$.

Determine whether $$$1600$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1600$$$ by $$${\color{green}2}$$$: $$$\frac{1600}{2} = {\color{red}800}$$$.

Determine whether $$$800$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$800$$$ by $$${\color{green}2}$$$: $$$\frac{800}{2} = {\color{red}400}$$$.

Determine whether $$$400$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$400$$$ by $$${\color{green}2}$$$: $$$\frac{400}{2} = {\color{red}200}$$$.

Determine whether $$$200$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$200$$$ by $$${\color{green}2}$$$: $$$\frac{200}{2} = {\color{red}100}$$$.

Determine whether $$$100$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$100$$$ by $$${\color{green}2}$$$: $$$\frac{100}{2} = {\color{red}50}$$$.

Determine whether $$$50$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$50$$$ by $$${\color{green}2}$$$: $$$\frac{50}{2} = {\color{red}25}$$$.

Determine whether $$$25$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$25$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$25$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$25$$$ by $$${\color{green}5}$$$: $$$\frac{25}{5} = {\color{red}5}$$$.

The prime number $$${\color{green}5}$$$ has no other factors then $$$1$$$ and $$${\color{green}5}$$$: $$$\frac{5}{5} = {\color{red}1}$$$.

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: $$$3200 = 2^{7} \cdot 5^{2}$$$.

The prime factorization is $$$3200 = 2^{7} \cdot 5^{2}$$$A.