# Prime factorization of $3174$

The calculator will find the prime factorization of $3174$, with steps shown.

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Find the prime factorization of $3174$.

### Solution

Start with the number $2$.

Determine whether $3174$ is divisible by $2$.

It is divisible, thus, divide $3174$ by ${\color{green}2}$: $\frac{3174}{2} = {\color{red}1587}$.

Determine whether $1587$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1587$ is divisible by $3$.

It is divisible, thus, divide $1587$ by ${\color{green}3}$: $\frac{1587}{3} = {\color{red}529}$.

Determine whether $529$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $529$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $529$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $529$ is divisible by $11$.

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

The next prime number is $13$.

Determine whether $529$ is divisible by $13$.

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

The next prime number is $17$.

Determine whether $529$ is divisible by $17$.

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

The next prime number is $19$.

Determine whether $529$ is divisible by $19$.

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

The next prime number is $23$.

Determine whether $529$ is divisible by $23$.

It is divisible, thus, divide $529$ by ${\color{green}23}$: $\frac{529}{23} = {\color{red}23}$.

The prime number ${\color{green}23}$ has no other factors then $1$ and ${\color{green}23}$: $\frac{23}{23} = {\color{red}1}$.

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: $3174 = 2 \cdot 3 \cdot 23^{2}$.

The prime factorization is $3174 = 2 \cdot 3 \cdot 23^{2}$A.