Prime factorization of $$$2888$$$
Your Input
Find the prime factorization of $$$2888$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$2888$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$2888$$$ by $$${\color{green}2}$$$: $$$\frac{2888}{2} = {\color{red}1444}$$$.
Determine whether $$$1444$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$1444$$$ by $$${\color{green}2}$$$: $$$\frac{1444}{2} = {\color{red}722}$$$.
Determine whether $$$722$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$722$$$ by $$${\color{green}2}$$$: $$$\frac{722}{2} = {\color{red}361}$$$.
Determine whether $$$361$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$361$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$361$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$361$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$361$$$ is divisible by $$$11$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$13$$$.
Determine whether $$$361$$$ is divisible by $$$13$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$17$$$.
Determine whether $$$361$$$ is divisible by $$$17$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$19$$$.
Determine whether $$$361$$$ is divisible by $$$19$$$.
It is divisible, thus, divide $$$361$$$ by $$${\color{green}19}$$$: $$$\frac{361}{19} = {\color{red}19}$$$.
The prime number $$${\color{green}19}$$$ has no other factors then $$$1$$$ and $$${\color{green}19}$$$: $$$\frac{19}{19} = {\color{red}1}$$$.
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: $$$2888 = 2^{3} \cdot 19^{2}$$$.
Answer
The prime factorization is $$$2888 = 2^{3} \cdot 19^{2}$$$A.