Prime factorization of $$$4109$$$

Find the prime factorization of $$$4109$$$.

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

Determine whether $$$4109$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$4109$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$4109$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$4109$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$4109$$$ by $$${\color{green}7}$$$: $$$\frac{4109}{7} = {\color{red}587}$$$.

The prime number $$${\color{green}587}$$$ has no other factors then $$$1$$$ and $$${\color{green}587}$$$: $$$\frac{587}{587} = {\color{red}1}$$$.

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: $$$4109 = 7 \cdot 587$$$.

The prime factorization is $$$4109 = 7 \cdot 587$$$A.