Prime factorization of $$$1395$$$
Your Input
Find the prime factorization of $$$1395$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$1395$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$1395$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$1395$$$ by $$${\color{green}3}$$$: $$$\frac{1395}{3} = {\color{red}465}$$$.
Determine whether $$$465$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$465$$$ by $$${\color{green}3}$$$: $$$\frac{465}{3} = {\color{red}155}$$$.
Determine whether $$$155$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$155$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$155$$$ by $$${\color{green}5}$$$: $$$\frac{155}{5} = {\color{red}31}$$$.
The prime number $$${\color{green}31}$$$ has no other factors then $$$1$$$ and $$${\color{green}31}$$$: $$$\frac{31}{31} = {\color{red}1}$$$.
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: $$$1395 = 3^{2} \cdot 5 \cdot 31$$$.
Answer
The prime factorization is $$$1395 = 3^{2} \cdot 5 \cdot 31$$$A.