Prime factorization of $$$3094$$$

Find the prime factorization of $$$3094$$$.

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

Determine whether $$$3094$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3094$$$ by $$${\color{green}2}$$$: $$$\frac{3094}{2} = {\color{red}1547}$$$.

Determine whether $$$1547$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1547$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1547$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$1547$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$1547$$$ by $$${\color{green}7}$$$: $$$\frac{1547}{7} = {\color{red}221}$$$.

Determine whether $$$221$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$221$$$ is divisible by $$$11$$$.

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

The next prime number is $$$13$$$.

Determine whether $$$221$$$ is divisible by $$$13$$$.

It is divisible, thus, divide $$$221$$$ by $$${\color{green}13}$$$: $$$\frac{221}{13} = {\color{red}17}$$$.

The prime number $$${\color{green}17}$$$ has no other factors then $$$1$$$ and $$${\color{green}17}$$$: $$$\frac{17}{17} = {\color{red}1}$$$.

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: $$$3094 = 2 \cdot 7 \cdot 13 \cdot 17$$$.

The prime factorization is $$$3094 = 2 \cdot 7 \cdot 13 \cdot 17$$$A.