# Prime factorization of $2780$

The calculator will find the prime factorization of $2780$, with steps shown.

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Find the prime factorization of $2780$.

### Solution

Start with the number $2$.

Determine whether $2780$ is divisible by $2$.

It is divisible, thus, divide $2780$ by ${\color{green}2}$: $\frac{2780}{2} = {\color{red}1390}$.

Determine whether $1390$ is divisible by $2$.

It is divisible, thus, divide $1390$ by ${\color{green}2}$: $\frac{1390}{2} = {\color{red}695}$.

Determine whether $695$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $695$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $695$ is divisible by $5$.

It is divisible, thus, divide $695$ by ${\color{green}5}$: $\frac{695}{5} = {\color{red}139}$.

The prime number ${\color{green}139}$ has no other factors then $1$ and ${\color{green}139}$: $\frac{139}{139} = {\color{red}1}$.

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: $2780 = 2^{2} \cdot 5 \cdot 139$.

The prime factorization is $2780 = 2^{2} \cdot 5 \cdot 139$A.