Prime factorization of $$$4345$$$
Your Input
Find the prime factorization of $$$4345$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$4345$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$4345$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$4345$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$4345$$$ by $$${\color{green}5}$$$: $$$\frac{4345}{5} = {\color{red}869}$$$.
Determine whether $$$869$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$869$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$869$$$ is divisible by $$$11$$$.
It is divisible, thus, divide $$$869$$$ by $$${\color{green}11}$$$: $$$\frac{869}{11} = {\color{red}79}$$$.
The prime number $$${\color{green}79}$$$ has no other factors then $$$1$$$ and $$${\color{green}79}$$$: $$$\frac{79}{79} = {\color{red}1}$$$.
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: $$$4345 = 5 \cdot 11 \cdot 79$$$.
Answer
The prime factorization is $$$4345 = 5 \cdot 11 \cdot 79$$$A.