Prime factorization of $$$2630$$$

Find the prime factorization of $$$2630$$$.

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

Determine whether $$$2630$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2630$$$ by $$${\color{green}2}$$$: $$$\frac{2630}{2} = {\color{red}1315}$$$.

Determine whether $$$1315$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1315$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1315$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$1315$$$ by $$${\color{green}5}$$$: $$$\frac{1315}{5} = {\color{red}263}$$$.

The prime number $$${\color{green}263}$$$ has no other factors then $$$1$$$ and $$${\color{green}263}$$$: $$$\frac{263}{263} = {\color{red}1}$$$.

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: $$$2630 = 2 \cdot 5 \cdot 263$$$.

The prime factorization is $$$2630 = 2 \cdot 5 \cdot 263$$$A.