Prime factorization of $$$1146$$$

Find the prime factorization of $$$1146$$$.

Start with the number $$$2$$$.

Determine whether $$$1146$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1146$$$ by $$${\color{green}2}$$$: $$$\frac{1146}{2} = {\color{red}573}$$$.

Determine whether $$$573$$$ is divisible by $$$2$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$3$$$.

Determine whether $$$573$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$573$$$ by $$${\color{green}3}$$$: $$$\frac{573}{3} = {\color{red}191}$$$.

The prime number $$${\color{green}191}$$$ has no other factors then $$$1$$$ and $$${\color{green}191}$$$: $$$\frac{191}{191} = {\color{red}1}$$$.

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: $$$1146 = 2 \cdot 3 \cdot 191$$$.

The prime factorization is $$$1146 = 2 \cdot 3 \cdot 191$$$A.