# Prime factorization of $3165$

The calculator will find the prime factorization of $3165$, with steps shown.

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Find the prime factorization of $3165$.

### Solution

Start with the number $2$.

Determine whether $3165$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $3165$ is divisible by $3$.

It is divisible, thus, divide $3165$ by ${\color{green}3}$: $\frac{3165}{3} = {\color{red}1055}$.

Determine whether $1055$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $1055$ is divisible by $5$.

It is divisible, thus, divide $1055$ by ${\color{green}5}$: $\frac{1055}{5} = {\color{red}211}$.

The prime number ${\color{green}211}$ has no other factors then $1$ and ${\color{green}211}$: $\frac{211}{211} = {\color{red}1}$.

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: $3165 = 3 \cdot 5 \cdot 211$.

The prime factorization is $3165 = 3 \cdot 5 \cdot 211$A.