# Prime factorization of $714$

The calculator will find the prime factorization of $714$, with steps shown.

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Find the prime factorization of $714$.

### Solution

Start with the number $2$.

Determine whether $714$ is divisible by $2$.

It is divisible, thus, divide $714$ by ${\color{green}2}$: $\frac{714}{2} = {\color{red}357}$.

Determine whether $357$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $357$ is divisible by $3$.

It is divisible, thus, divide $357$ by ${\color{green}3}$: $\frac{357}{3} = {\color{red}119}$.

Determine whether $119$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $119$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $119$ is divisible by $7$.

It is divisible, thus, divide $119$ by ${\color{green}7}$: $\frac{119}{7} = {\color{red}17}$.

The prime number ${\color{green}17}$ has no other factors then $1$ and ${\color{green}17}$: $\frac{17}{17} = {\color{red}1}$.

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: $714 = 2 \cdot 3 \cdot 7 \cdot 17$.

The prime factorization is $714 = 2 \cdot 3 \cdot 7 \cdot 17$A.