# Prime factorization of $2782$

The calculator will find the prime factorization of $2782$, with steps shown.

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Find the prime factorization of $2782$.

### Solution

Start with the number $2$.

Determine whether $2782$ is divisible by $2$.

It is divisible, thus, divide $2782$ by ${\color{green}2}$: $\frac{2782}{2} = {\color{red}1391}$.

Determine whether $1391$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1391$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $1391$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $1391$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $1391$ is divisible by $11$.

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

The next prime number is $13$.

Determine whether $1391$ is divisible by $13$.

It is divisible, thus, divide $1391$ by ${\color{green}13}$: $\frac{1391}{13} = {\color{red}107}$.

The prime number ${\color{green}107}$ has no other factors then $1$ and ${\color{green}107}$: $\frac{107}{107} = {\color{red}1}$.

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: $2782 = 2 \cdot 13 \cdot 107$.

The prime factorization is $2782 = 2 \cdot 13 \cdot 107$A.