Prime factorization of $$$240$$$
Your Input
Find the prime factorization of $$$240$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$240$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$240$$$ by $$${\color{green}2}$$$: $$$\frac{240}{2} = {\color{red}120}$$$.
Determine whether $$$120$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$120$$$ by $$${\color{green}2}$$$: $$$\frac{120}{2} = {\color{red}60}$$$.
Determine whether $$$60$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$60$$$ by $$${\color{green}2}$$$: $$$\frac{60}{2} = {\color{red}30}$$$.
Determine whether $$$30$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$30$$$ by $$${\color{green}2}$$$: $$$\frac{30}{2} = {\color{red}15}$$$.
Determine whether $$$15$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$15$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$15$$$ by $$${\color{green}3}$$$: $$$\frac{15}{3} = {\color{red}5}$$$.
The prime number $$${\color{green}5}$$$ has no other factors then $$$1$$$ and $$${\color{green}5}$$$: $$$\frac{5}{5} = {\color{red}1}$$$.
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: $$$240 = 2^{4} \cdot 3 \cdot 5$$$.
Answer
The prime factorization is $$$240 = 2^{4} \cdot 3 \cdot 5$$$A.