Prime factorization of $$$4418$$$

Find the prime factorization of $$$4418$$$.

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

Determine whether $$$4418$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4418$$$ by $$${\color{green}2}$$$: $$$\frac{4418}{2} = {\color{red}2209}$$$.

Determine whether $$$2209$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2209$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$2209$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$2209$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$2209$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$2209$$$ is divisible by $$$13$$$.

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

The next prime number is $$$17$$$.

Determine whether $$$2209$$$ is divisible by $$$17$$$.

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

The next prime number is $$$19$$$.

Determine whether $$$2209$$$ is divisible by $$$19$$$.

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

The next prime number is $$$23$$$.

Determine whether $$$2209$$$ is divisible by $$$23$$$.

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

The next prime number is $$$29$$$.

Determine whether $$$2209$$$ is divisible by $$$29$$$.

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

The next prime number is $$$31$$$.

Determine whether $$$2209$$$ is divisible by $$$31$$$.

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

The next prime number is $$$37$$$.

Determine whether $$$2209$$$ is divisible by $$$37$$$.

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

The next prime number is $$$41$$$.

Determine whether $$$2209$$$ is divisible by $$$41$$$.

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

The next prime number is $$$43$$$.

Determine whether $$$2209$$$ is divisible by $$$43$$$.

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

The next prime number is $$$47$$$.

Determine whether $$$2209$$$ is divisible by $$$47$$$.

It is divisible, thus, divide $$$2209$$$ by $$${\color{green}47}$$$: $$$\frac{2209}{47} = {\color{red}47}$$$.

The prime number $$${\color{green}47}$$$ has no other factors then $$$1$$$ and $$${\color{green}47}$$$: $$$\frac{47}{47} = {\color{red}1}$$$.

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: $$$4418 = 2 \cdot 47^{2}$$$.

The prime factorization is $$$4418 = 2 \cdot 47^{2}$$$A.