# Prime factorization of $3177$

The calculator will find the prime factorization of $3177$, with steps shown.

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Find the prime factorization of $3177$.

### Solution

Start with the number $2$.

Determine whether $3177$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $3177$ is divisible by $3$.

It is divisible, thus, divide $3177$ by ${\color{green}3}$: $\frac{3177}{3} = {\color{red}1059}$.

Determine whether $1059$ is divisible by $3$.

It is divisible, thus, divide $1059$ by ${\color{green}3}$: $\frac{1059}{3} = {\color{red}353}$.

The prime number ${\color{green}353}$ has no other factors then $1$ and ${\color{green}353}$: $\frac{353}{353} = {\color{red}1}$.

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: $3177 = 3^{2} \cdot 353$.

The prime factorization is $3177 = 3^{2} \cdot 353$A.