Prime factorization of $$$1330$$$

Find the prime factorization of $$$1330$$$.

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

Determine whether $$$1330$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1330$$$ by $$${\color{green}2}$$$: $$$\frac{1330}{2} = {\color{red}665}$$$.

Determine whether $$$665$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$665$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$665$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$665$$$ by $$${\color{green}5}$$$: $$$\frac{665}{5} = {\color{red}133}$$$.

Determine whether $$$133$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$133$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$133$$$ by $$${\color{green}7}$$$: $$$\frac{133}{7} = {\color{red}19}$$$.

The prime number $$${\color{green}19}$$$ has no other factors then $$$1$$$ and $$${\color{green}19}$$$: $$$\frac{19}{19} = {\color{red}1}$$$.

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: $$$1330 = 2 \cdot 5 \cdot 7 \cdot 19$$$.

The prime factorization is $$$1330 = 2 \cdot 5 \cdot 7 \cdot 19$$$A.