Prime factorization of $$$1589$$$
Your Input
Find the prime factorization of $$$1589$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$1589$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$1589$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$1589$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$1589$$$ is divisible by $$$7$$$.
It is divisible, thus, divide $$$1589$$$ by $$${\color{green}7}$$$: $$$\frac{1589}{7} = {\color{red}227}$$$.
The prime number $$${\color{green}227}$$$ has no other factors then $$$1$$$ and $$${\color{green}227}$$$: $$$\frac{227}{227} = {\color{red}1}$$$.
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: $$$1589 = 7 \cdot 227$$$.
Answer
The prime factorization is $$$1589 = 7 \cdot 227$$$A.