Prime factorization of $$$2233$$$

Find the prime factorization of $$$2233$$$.

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

Determine whether $$$2233$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2233$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$2233$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$2233$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$2233$$$ by $$${\color{green}7}$$$: $$$\frac{2233}{7} = {\color{red}319}$$$.

Determine whether $$$319$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$319$$$ is divisible by $$$11$$$.

It is divisible, thus, divide $$$319$$$ by $$${\color{green}11}$$$: $$$\frac{319}{11} = {\color{red}29}$$$.

The prime number $$${\color{green}29}$$$ has no other factors then $$$1$$$ and $$${\color{green}29}$$$: $$$\frac{29}{29} = {\color{red}1}$$$.

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: $$$2233 = 7 \cdot 11 \cdot 29$$$.

The prime factorization is $$$2233 = 7 \cdot 11 \cdot 29$$$A.