Prime factorization of $$$2893$$$

Find the prime factorization of $$$2893$$$.

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

Determine whether $$$2893$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2893$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$2893$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$2893$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$2893$$$ is divisible by $$$11$$$.

It is divisible, thus, divide $$$2893$$$ by $$${\color{green}11}$$$: $$$\frac{2893}{11} = {\color{red}263}$$$.

The prime number $$${\color{green}263}$$$ has no other factors then $$$1$$$ and $$${\color{green}263}$$$: $$$\frac{263}{263} = {\color{red}1}$$$.

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: $$$2893 = 11 \cdot 263$$$.

The prime factorization is $$$2893 = 11 \cdot 263$$$A.