# Prime factorization of $3190$

The calculator will find the prime factorization of $3190$, with steps shown.

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Find the prime factorization of $3190$.

### Solution

Start with the number $2$.

Determine whether $3190$ is divisible by $2$.

It is divisible, thus, divide $3190$ by ${\color{green}2}$: $\frac{3190}{2} = {\color{red}1595}$.

Determine whether $1595$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1595$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $1595$ is divisible by $5$.

It is divisible, thus, divide $1595$ by ${\color{green}5}$: $\frac{1595}{5} = {\color{red}319}$.

Determine whether $319$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $319$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $319$ is divisible by $11$.

It is divisible, thus, divide $319$ by ${\color{green}11}$: $\frac{319}{11} = {\color{red}29}$.

The prime number ${\color{green}29}$ has no other factors then $1$ and ${\color{green}29}$: $\frac{29}{29} = {\color{red}1}$.

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: $3190 = 2 \cdot 5 \cdot 11 \cdot 29$.

The prime factorization is $3190 = 2 \cdot 5 \cdot 11 \cdot 29$A.