Prime factorization of $$$3680$$$

Find the prime factorization of $$$3680$$$.

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

Determine whether $$$3680$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3680$$$ by $$${\color{green}2}$$$: $$$\frac{3680}{2} = {\color{red}1840}$$$.

Determine whether $$$1840$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1840$$$ by $$${\color{green}2}$$$: $$$\frac{1840}{2} = {\color{red}920}$$$.

Determine whether $$$920$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$920$$$ by $$${\color{green}2}$$$: $$$\frac{920}{2} = {\color{red}460}$$$.

Determine whether $$$460$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$460$$$ by $$${\color{green}2}$$$: $$$\frac{460}{2} = {\color{red}230}$$$.

Determine whether $$$230$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$230$$$ by $$${\color{green}2}$$$: $$$\frac{230}{2} = {\color{red}115}$$$.

Determine whether $$$115$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$115$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$115$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$115$$$ by $$${\color{green}5}$$$: $$$\frac{115}{5} = {\color{red}23}$$$.

The prime number $$${\color{green}23}$$$ has no other factors then $$$1$$$ and $$${\color{green}23}$$$: $$$\frac{23}{23} = {\color{red}1}$$$.

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: $$$3680 = 2^{5} \cdot 5 \cdot 23$$$.

The prime factorization is $$$3680 = 2^{5} \cdot 5 \cdot 23$$$A.