Prime factorization of $$$1582$$$

Find the prime factorization of $$$1582$$$.

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

Determine whether $$$1582$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1582$$$ by $$${\color{green}2}$$$: $$$\frac{1582}{2} = {\color{red}791}$$$.

Determine whether $$$791$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$791$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$791$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$791$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$791$$$ by $$${\color{green}7}$$$: $$$\frac{791}{7} = {\color{red}113}$$$.

The prime number $$${\color{green}113}$$$ has no other factors then $$$1$$$ and $$${\color{green}113}$$$: $$$\frac{113}{113} = {\color{red}1}$$$.

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: $$$1582 = 2 \cdot 7 \cdot 113$$$.

The prime factorization is $$$1582 = 2 \cdot 7 \cdot 113$$$A.