# Prime factorization of $2212$

The calculator will find the prime factorization of $2212$, with steps shown.

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Find the prime factorization of $2212$.

### Solution

Start with the number $2$.

Determine whether $2212$ is divisible by $2$.

It is divisible, thus, divide $2212$ by ${\color{green}2}$: $\frac{2212}{2} = {\color{red}1106}$.

Determine whether $1106$ is divisible by $2$.

It is divisible, thus, divide $1106$ by ${\color{green}2}$: $\frac{1106}{2} = {\color{red}553}$.

Determine whether $553$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $553$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $553$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $553$ is divisible by $7$.

It is divisible, thus, divide $553$ by ${\color{green}7}$: $\frac{553}{7} = {\color{red}79}$.

The prime number ${\color{green}79}$ has no other factors then $1$ and ${\color{green}79}$: $\frac{79}{79} = {\color{red}1}$.

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: $2212 = 2^{2} \cdot 7 \cdot 79$.

The prime factorization is $2212 = 2^{2} \cdot 7 \cdot 79$A.