Prime factorization of $$$880$$$

Find the prime factorization of $$$880$$$.

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

Determine whether $$$880$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$880$$$ by $$${\color{green}2}$$$: $$$\frac{880}{2} = {\color{red}440}$$$.

Determine whether $$$440$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$440$$$ by $$${\color{green}2}$$$: $$$\frac{440}{2} = {\color{red}220}$$$.

Determine whether $$$220$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$220$$$ by $$${\color{green}2}$$$: $$$\frac{220}{2} = {\color{red}110}$$$.

Determine whether $$$110$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$110$$$ by $$${\color{green}2}$$$: $$$\frac{110}{2} = {\color{red}55}$$$.

Determine whether $$$55$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$55$$$ is divisible by $$$3$$$.

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

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

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: $$$880 = 2^{4} \cdot 5 \cdot 11$$$.

The prime factorization is $$$880 = 2^{4} \cdot 5 \cdot 11$$$A.