Prime factorization of $$$2574$$$
Your Input
Find the prime factorization of $$$2574$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$2574$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$2574$$$ by $$${\color{green}2}$$$: $$$\frac{2574}{2} = {\color{red}1287}$$$.
Determine whether $$$1287$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$1287$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$1287$$$ by $$${\color{green}3}$$$: $$$\frac{1287}{3} = {\color{red}429}$$$.
Determine whether $$$429$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$429$$$ by $$${\color{green}3}$$$: $$$\frac{429}{3} = {\color{red}143}$$$.
Determine whether $$$143$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$143$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$143$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$143$$$ is divisible by $$$11$$$.
It is divisible, thus, divide $$$143$$$ by $$${\color{green}11}$$$: $$$\frac{143}{11} = {\color{red}13}$$$.
The prime number $$${\color{green}13}$$$ has no other factors then $$$1$$$ and $$${\color{green}13}$$$: $$$\frac{13}{13} = {\color{red}1}$$$.
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: $$$2574 = 2 \cdot 3^{2} \cdot 11 \cdot 13$$$.
Answer
The prime factorization is $$$2574 = 2 \cdot 3^{2} \cdot 11 \cdot 13$$$A.