Prime factorization of $$$2200$$$

Find the prime factorization of $$$2200$$$.

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

Determine whether $$$2200$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2200$$$ by $$${\color{green}2}$$$: $$$\frac{2200}{2} = {\color{red}1100}$$$.

Determine whether $$$1100$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1100$$$ by $$${\color{green}2}$$$: $$$\frac{1100}{2} = {\color{red}550}$$$.

Determine whether $$$550$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$550$$$ by $$${\color{green}2}$$$: $$$\frac{550}{2} = {\color{red}275}$$$.

Determine whether $$$275$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$275$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$275$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$275$$$ by $$${\color{green}5}$$$: $$$\frac{275}{5} = {\color{red}55}$$$.

Determine whether $$$55$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$55$$$ by $$${\color{green}5}$$$: $$$\frac{55}{5} = {\color{red}11}$$$.

The prime number $$${\color{green}11}$$$ has no other factors then $$$1$$$ and $$${\color{green}11}$$$: $$$\frac{11}{11} = {\color{red}1}$$$.

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: $$$2200 = 2^{3} \cdot 5^{2} \cdot 11$$$.

The prime factorization is $$$2200 = 2^{3} \cdot 5^{2} \cdot 11$$$A.