Prime factorization of $$$1258$$$
Your Input
Find the prime factorization of $$$1258$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$1258$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$1258$$$ by $$${\color{green}2}$$$: $$$\frac{1258}{2} = {\color{red}629}$$$.
Determine whether $$$629$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$629$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$629$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$629$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$629$$$ is divisible by $$$11$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$13$$$.
Determine whether $$$629$$$ is divisible by $$$13$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$17$$$.
Determine whether $$$629$$$ is divisible by $$$17$$$.
It is divisible, thus, divide $$$629$$$ by $$${\color{green}17}$$$: $$$\frac{629}{17} = {\color{red}37}$$$.
The prime number $$${\color{green}37}$$$ has no other factors then $$$1$$$ and $$${\color{green}37}$$$: $$$\frac{37}{37} = {\color{red}1}$$$.
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: $$$1258 = 2 \cdot 17 \cdot 37$$$.
Answer
The prime factorization is $$$1258 = 2 \cdot 17 \cdot 37$$$A.