# Prime factorization of $217$

The calculator will find the prime factorization of $217$, with steps shown.

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Find the prime factorization of $217$.

### Solution

Start with the number $2$.

Determine whether $217$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $217$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $217$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $217$ is divisible by $7$.

It is divisible, thus, divide $217$ by ${\color{green}7}$: $\frac{217}{7} = {\color{red}31}$.

The prime number ${\color{green}31}$ has no other factors then $1$ and ${\color{green}31}$: $\frac{31}{31} = {\color{red}1}$.

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: $217 = 7 \cdot 31$.

The prime factorization is $217 = 7 \cdot 31$A.