Prime factorization of $$$994$$$

Find the prime factorization of $$$994$$$.

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

Determine whether $$$994$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$994$$$ by $$${\color{green}2}$$$: $$$\frac{994}{2} = {\color{red}497}$$$.

Determine whether $$$497$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$497$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$497$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$497$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$497$$$ by $$${\color{green}7}$$$: $$$\frac{497}{7} = {\color{red}71}$$$.

The prime number $$${\color{green}71}$$$ has no other factors then $$$1$$$ and $$${\color{green}71}$$$: $$$\frac{71}{71} = {\color{red}1}$$$.

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: $$$994 = 2 \cdot 7 \cdot 71$$$.

The prime factorization is $$$994 = 2 \cdot 7 \cdot 71$$$A.