Prime factorization of $$$3619$$$
Your Input
Find the prime factorization of $$$3619$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$3619$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$3619$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$3619$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$3619$$$ is divisible by $$$7$$$.
It is divisible, thus, divide $$$3619$$$ by $$${\color{green}7}$$$: $$$\frac{3619}{7} = {\color{red}517}$$$.
Determine whether $$$517$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$517$$$ is divisible by $$$11$$$.
It is divisible, thus, divide $$$517$$$ by $$${\color{green}11}$$$: $$$\frac{517}{11} = {\color{red}47}$$$.
The prime number $$${\color{green}47}$$$ has no other factors then $$$1$$$ and $$${\color{green}47}$$$: $$$\frac{47}{47} = {\color{red}1}$$$.
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: $$$3619 = 7 \cdot 11 \cdot 47$$$.
Answer
The prime factorization is $$$3619 = 7 \cdot 11 \cdot 47$$$A.