Prime factorization of $$$1353$$$
Your Input
Find the prime factorization of $$$1353$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$1353$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$1353$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$1353$$$ by $$${\color{green}3}$$$: $$$\frac{1353}{3} = {\color{red}451}$$$.
Determine whether $$$451$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$451$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$451$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$451$$$ is divisible by $$$11$$$.
It is divisible, thus, divide $$$451$$$ by $$${\color{green}11}$$$: $$$\frac{451}{11} = {\color{red}41}$$$.
The prime number $$${\color{green}41}$$$ has no other factors then $$$1$$$ and $$${\color{green}41}$$$: $$$\frac{41}{41} = {\color{red}1}$$$.
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: $$$1353 = 3 \cdot 11 \cdot 41$$$.
Answer
The prime factorization is $$$1353 = 3 \cdot 11 \cdot 41$$$A.