Prime factorization of $$$2149$$$

Find the prime factorization of $$$2149$$$.

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

Determine whether $$$2149$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2149$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$2149$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$2149$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$2149$$$ by $$${\color{green}7}$$$: $$$\frac{2149}{7} = {\color{red}307}$$$.

The prime number $$${\color{green}307}$$$ has no other factors then $$$1$$$ and $$${\color{green}307}$$$: $$$\frac{307}{307} = {\color{red}1}$$$.

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: $$$2149 = 7 \cdot 307$$$.

The prime factorization is $$$2149 = 7 \cdot 307$$$A.