Prime factorization of $$$4613$$$

Find the prime factorization of $$$4613$$$.

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

Determine whether $$$4613$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$4613$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$4613$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$4613$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$4613$$$ by $$${\color{green}7}$$$: $$$\frac{4613}{7} = {\color{red}659}$$$.

The prime number $$${\color{green}659}$$$ has no other factors then $$$1$$$ and $$${\color{green}659}$$$: $$$\frac{659}{659} = {\color{red}1}$$$.

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: $$$4613 = 7 \cdot 659$$$.

The prime factorization is $$$4613 = 7 \cdot 659$$$A.