Prime factorization of $$$2780$$$

Find the prime factorization of $$$2780$$$.

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

Determine whether $$$2780$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2780$$$ by $$${\color{green}2}$$$: $$$\frac{2780}{2} = {\color{red}1390}$$$.

Determine whether $$$1390$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1390$$$ by $$${\color{green}2}$$$: $$$\frac{1390}{2} = {\color{red}695}$$$.

Determine whether $$$695$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$695$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$695$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$695$$$ by $$${\color{green}5}$$$: $$$\frac{695}{5} = {\color{red}139}$$$.

The prime number $$${\color{green}139}$$$ has no other factors then $$$1$$$ and $$${\color{green}139}$$$: $$$\frac{139}{139} = {\color{red}1}$$$.

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: $$$2780 = 2^{2} \cdot 5 \cdot 139$$$.

The prime factorization is $$$2780 = 2^{2} \cdot 5 \cdot 139$$$A.