# Prime factorization of $2776$

The calculator will find the prime factorization of $2776$, with steps shown.

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Find the prime factorization of $2776$.

### Solution

Start with the number $2$.

Determine whether $2776$ is divisible by $2$.

It is divisible, thus, divide $2776$ by ${\color{green}2}$: $\frac{2776}{2} = {\color{red}1388}$.

Determine whether $1388$ is divisible by $2$.

It is divisible, thus, divide $1388$ by ${\color{green}2}$: $\frac{1388}{2} = {\color{red}694}$.

Determine whether $694$ is divisible by $2$.

It is divisible, thus, divide $694$ by ${\color{green}2}$: $\frac{694}{2} = {\color{red}347}$.

The prime number ${\color{green}347}$ has no other factors then $1$ and ${\color{green}347}$: $\frac{347}{347} = {\color{red}1}$.

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: $2776 = 2^{3} \cdot 347$.

The prime factorization is $2776 = 2^{3} \cdot 347$A.