Prime factorization of $$$3320$$$

Find the prime factorization of $$$3320$$$.

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

Determine whether $$$3320$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3320$$$ by $$${\color{green}2}$$$: $$$\frac{3320}{2} = {\color{red}1660}$$$.

Determine whether $$$1660$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1660$$$ by $$${\color{green}2}$$$: $$$\frac{1660}{2} = {\color{red}830}$$$.

Determine whether $$$830$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$830$$$ by $$${\color{green}2}$$$: $$$\frac{830}{2} = {\color{red}415}$$$.

Determine whether $$$415$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$415$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$415$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$415$$$ by $$${\color{green}5}$$$: $$$\frac{415}{5} = {\color{red}83}$$$.

The prime number $$${\color{green}83}$$$ has no other factors then $$$1$$$ and $$${\color{green}83}$$$: $$$\frac{83}{83} = {\color{red}1}$$$.

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: $$$3320 = 2^{3} \cdot 5 \cdot 83$$$.

The prime factorization is $$$3320 = 2^{3} \cdot 5 \cdot 83$$$A.