Prime factorization of $$$1534$$$
Your Input
Find the prime factorization of $$$1534$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$1534$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$1534$$$ by $$${\color{green}2}$$$: $$$\frac{1534}{2} = {\color{red}767}$$$.
Determine whether $$$767$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$767$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$767$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$767$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$767$$$ is divisible by $$$11$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$13$$$.
Determine whether $$$767$$$ is divisible by $$$13$$$.
It is divisible, thus, divide $$$767$$$ by $$${\color{green}13}$$$: $$$\frac{767}{13} = {\color{red}59}$$$.
The prime number $$${\color{green}59}$$$ has no other factors then $$$1$$$ and $$${\color{green}59}$$$: $$$\frac{59}{59} = {\color{red}1}$$$.
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: $$$1534 = 2 \cdot 13 \cdot 59$$$.
Answer
The prime factorization is $$$1534 = 2 \cdot 13 \cdot 59$$$A.