# Prime factorization of $3776$

The calculator will find the prime factorization of $3776$, with steps shown.

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### Your Input

Find the prime factorization of $3776$.

### Solution

Start with the number $2$.

Determine whether $3776$ is divisible by $2$.

It is divisible, thus, divide $3776$ by ${\color{green}2}$: $\frac{3776}{2} = {\color{red}1888}$.

Determine whether $1888$ is divisible by $2$.

It is divisible, thus, divide $1888$ by ${\color{green}2}$: $\frac{1888}{2} = {\color{red}944}$.

Determine whether $944$ is divisible by $2$.

It is divisible, thus, divide $944$ by ${\color{green}2}$: $\frac{944}{2} = {\color{red}472}$.

Determine whether $472$ is divisible by $2$.

It is divisible, thus, divide $472$ by ${\color{green}2}$: $\frac{472}{2} = {\color{red}236}$.

Determine whether $236$ is divisible by $2$.

It is divisible, thus, divide $236$ by ${\color{green}2}$: $\frac{236}{2} = {\color{red}118}$.

Determine whether $118$ is divisible by $2$.

It is divisible, thus, divide $118$ by ${\color{green}2}$: $\frac{118}{2} = {\color{red}59}$.

The prime number ${\color{green}59}$ has no other factors then $1$ and ${\color{green}59}$: $\frac{59}{59} = {\color{red}1}$.

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: $3776 = 2^{6} \cdot 59$.

### Answer

The prime factorization is $3776 = 2^{6} \cdot 59$A.