Prime factorization of $$$2977$$$

Find the prime factorization of $$$2977$$$.

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

Determine whether $$$2977$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2977$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$2977$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$2977$$$ is divisible by $$$7$$$.

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

The next prime number is $$$11$$$.

Determine whether $$$2977$$$ is divisible by $$$11$$$.

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

The next prime number is $$$13$$$.

Determine whether $$$2977$$$ is divisible by $$$13$$$.

It is divisible, thus, divide $$$2977$$$ by $$${\color{green}13}$$$: $$$\frac{2977}{13} = {\color{red}229}$$$.

The prime number $$${\color{green}229}$$$ has no other factors then $$$1$$$ and $$${\color{green}229}$$$: $$$\frac{229}{229} = {\color{red}1}$$$.

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: $$$2977 = 13 \cdot 229$$$.

The prime factorization is $$$2977 = 13 \cdot 229$$$A.