Prime factorization of $$$1302$$$

Find the prime factorization of $$$1302$$$.

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

Determine whether $$$1302$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1302$$$ by $$${\color{green}2}$$$: $$$\frac{1302}{2} = {\color{red}651}$$$.

Determine whether $$$651$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$651$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$651$$$ by $$${\color{green}3}$$$: $$$\frac{651}{3} = {\color{red}217}$$$.

Determine whether $$$217$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$217$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$217$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$217$$$ by $$${\color{green}7}$$$: $$$\frac{217}{7} = {\color{red}31}$$$.

The prime number $$${\color{green}31}$$$ has no other factors then $$$1$$$ and $$${\color{green}31}$$$: $$$\frac{31}{31} = {\color{red}1}$$$.

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: $$$1302 = 2 \cdot 3 \cdot 7 \cdot 31$$$.

The prime factorization is $$$1302 = 2 \cdot 3 \cdot 7 \cdot 31$$$A.