Prime factorization of $$$2274$$$

Find the prime factorization of $$$2274$$$.

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

Determine whether $$$2274$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2274$$$ by $$${\color{green}2}$$$: $$$\frac{2274}{2} = {\color{red}1137}$$$.

Determine whether $$$1137$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1137$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1137$$$ by $$${\color{green}3}$$$: $$$\frac{1137}{3} = {\color{red}379}$$$.

The prime number $$${\color{green}379}$$$ has no other factors then $$$1$$$ and $$${\color{green}379}$$$: $$$\frac{379}{379} = {\color{red}1}$$$.

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: $$$2274 = 2 \cdot 3 \cdot 379$$$.

The prime factorization is $$$2274 = 2 \cdot 3 \cdot 379$$$A.