Prime factorization of $$$2590$$$

Find the prime factorization of $$$2590$$$.

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

Determine whether $$$2590$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2590$$$ by $$${\color{green}2}$$$: $$$\frac{2590}{2} = {\color{red}1295}$$$.

Determine whether $$$1295$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1295$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1295$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$1295$$$ by $$${\color{green}5}$$$: $$$\frac{1295}{5} = {\color{red}259}$$$.

Determine whether $$$259$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$259$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$259$$$ by $$${\color{green}7}$$$: $$$\frac{259}{7} = {\color{red}37}$$$.

The prime number $$${\color{green}37}$$$ has no other factors then $$$1$$$ and $$${\color{green}37}$$$: $$$\frac{37}{37} = {\color{red}1}$$$.

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: $$$2590 = 2 \cdot 5 \cdot 7 \cdot 37$$$.

The prime factorization is $$$2590 = 2 \cdot 5 \cdot 7 \cdot 37$$$A.