Prime factorization of $$$1505$$$
Your Input
Find the prime factorization of $$$1505$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$1505$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$1505$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$1505$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$1505$$$ by $$${\color{green}5}$$$: $$$\frac{1505}{5} = {\color{red}301}$$$.
Determine whether $$$301$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$301$$$ is divisible by $$$7$$$.
It is divisible, thus, divide $$$301$$$ by $$${\color{green}7}$$$: $$$\frac{301}{7} = {\color{red}43}$$$.
The prime number $$${\color{green}43}$$$ has no other factors then $$$1$$$ and $$${\color{green}43}$$$: $$$\frac{43}{43} = {\color{red}1}$$$.
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: $$$1505 = 5 \cdot 7 \cdot 43$$$.
Answer
The prime factorization is $$$1505 = 5 \cdot 7 \cdot 43$$$A.