Prime factorization of $$$2835$$$
Your Input
Find the prime factorization of $$$2835$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$2835$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$2835$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$2835$$$ by $$${\color{green}3}$$$: $$$\frac{2835}{3} = {\color{red}945}$$$.
Determine whether $$$945$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$945$$$ by $$${\color{green}3}$$$: $$$\frac{945}{3} = {\color{red}315}$$$.
Determine whether $$$315$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$315$$$ by $$${\color{green}3}$$$: $$$\frac{315}{3} = {\color{red}105}$$$.
Determine whether $$$105$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$105$$$ by $$${\color{green}3}$$$: $$$\frac{105}{3} = {\color{red}35}$$$.
Determine whether $$$35$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$35$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$35$$$ by $$${\color{green}5}$$$: $$$\frac{35}{5} = {\color{red}7}$$$.
The prime number $$${\color{green}7}$$$ has no other factors then $$$1$$$ and $$${\color{green}7}$$$: $$$\frac{7}{7} = {\color{red}1}$$$.
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: $$$2835 = 3^{4} \cdot 5 \cdot 7$$$.
Answer
The prime factorization is $$$2835 = 3^{4} \cdot 5 \cdot 7$$$A.