Prime factorization of $$$2366$$$

Find the prime factorization of $$$2366$$$.

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

Determine whether $$$2366$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2366$$$ by $$${\color{green}2}$$$: $$$\frac{2366}{2} = {\color{red}1183}$$$.

Determine whether $$$1183$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1183$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1183$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$1183$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$1183$$$ by $$${\color{green}7}$$$: $$$\frac{1183}{7} = {\color{red}169}$$$.

Determine whether $$$169$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$169$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$169$$$ is divisible by $$$13$$$.

It is divisible, thus, divide $$$169$$$ by $$${\color{green}13}$$$: $$$\frac{169}{13} = {\color{red}13}$$$.

The prime number $$${\color{green}13}$$$ has no other factors then $$$1$$$ and $$${\color{green}13}$$$: $$$\frac{13}{13} = {\color{red}1}$$$.

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: $$$2366 = 2 \cdot 7 \cdot 13^{2}$$$.

The prime factorization is $$$2366 = 2 \cdot 7 \cdot 13^{2}$$$A.