Prime factorization of $$$2198$$$

Find the prime factorization of $$$2198$$$.

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

Determine whether $$$2198$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2198$$$ by $$${\color{green}2}$$$: $$$\frac{2198}{2} = {\color{red}1099}$$$.

Determine whether $$$1099$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1099$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1099$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$1099$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$1099$$$ by $$${\color{green}7}$$$: $$$\frac{1099}{7} = {\color{red}157}$$$.

The prime number $$${\color{green}157}$$$ has no other factors then $$$1$$$ and $$${\color{green}157}$$$: $$$\frac{157}{157} = {\color{red}1}$$$.

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: $$$2198 = 2 \cdot 7 \cdot 157$$$.

The prime factorization is $$$2198 = 2 \cdot 7 \cdot 157$$$A.