Prime factorization of $$$4440$$$
Your Input
Find the prime factorization of $$$4440$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$4440$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$4440$$$ by $$${\color{green}2}$$$: $$$\frac{4440}{2} = {\color{red}2220}$$$.
Determine whether $$$2220$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$2220$$$ by $$${\color{green}2}$$$: $$$\frac{2220}{2} = {\color{red}1110}$$$.
Determine whether $$$1110$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$1110$$$ by $$${\color{green}2}$$$: $$$\frac{1110}{2} = {\color{red}555}$$$.
Determine whether $$$555$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$555$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$555$$$ by $$${\color{green}3}$$$: $$$\frac{555}{3} = {\color{red}185}$$$.
Determine whether $$$185$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$185$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$185$$$ by $$${\color{green}5}$$$: $$$\frac{185}{5} = {\color{red}37}$$$.
The prime number $$${\color{green}37}$$$ has no other factors then $$$1$$$ and $$${\color{green}37}$$$: $$$\frac{37}{37} = {\color{red}1}$$$.
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: $$$4440 = 2^{3} \cdot 3 \cdot 5 \cdot 37$$$.
Answer
The prime factorization is $$$4440 = 2^{3} \cdot 3 \cdot 5 \cdot 37$$$A.