Prime factorization of $$$946$$$

Find the prime factorization of $$$946$$$.

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

Determine whether $$$946$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$946$$$ by $$${\color{green}2}$$$: $$$\frac{946}{2} = {\color{red}473}$$$.

Determine whether $$$473$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$473$$$ is divisible by $$$3$$$.

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

The next prime number is $$$5$$$.

Determine whether $$$473$$$ is divisible by $$$5$$$.

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

The next prime number is $$$7$$$.

Determine whether $$$473$$$ is divisible by $$$7$$$.

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

The next prime number is $$$11$$$.

Determine whether $$$473$$$ is divisible by $$$11$$$.

It is divisible, thus, divide $$$473$$$ by $$${\color{green}11}$$$: $$$\frac{473}{11} = {\color{red}43}$$$.

The prime number $$${\color{green}43}$$$ has no other factors then $$$1$$$ and $$${\color{green}43}$$$: $$$\frac{43}{43} = {\color{red}1}$$$.

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: $$$946 = 2 \cdot 11 \cdot 43$$$.

The prime factorization is $$$946 = 2 \cdot 11 \cdot 43$$$A.