# Prime factorization of $4422$

The calculator will find the prime factorization of $4422$, with steps shown.

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Find the prime factorization of $4422$.

### Solution

Start with the number $2$.

Determine whether $4422$ is divisible by $2$.

It is divisible, thus, divide $4422$ by ${\color{green}2}$: $\frac{4422}{2} = {\color{red}2211}$.

Determine whether $2211$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2211$ is divisible by $3$.

It is divisible, thus, divide $2211$ by ${\color{green}3}$: $\frac{2211}{3} = {\color{red}737}$.

Determine whether $737$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $737$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $737$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $737$ is divisible by $11$.

It is divisible, thus, divide $737$ by ${\color{green}11}$: $\frac{737}{11} = {\color{red}67}$.

The prime number ${\color{green}67}$ has no other factors then $1$ and ${\color{green}67}$: $\frac{67}{67} = {\color{red}1}$.

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: $4422 = 2 \cdot 3 \cdot 11 \cdot 67$.

The prime factorization is $4422 = 2 \cdot 3 \cdot 11 \cdot 67$A.