# Prime factorization of $3688$

The calculator will find the prime factorization of $3688$, with steps shown.

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Find the prime factorization of $3688$.

### Solution

Start with the number $2$.

Determine whether $3688$ is divisible by $2$.

It is divisible, thus, divide $3688$ by ${\color{green}2}$: $\frac{3688}{2} = {\color{red}1844}$.

Determine whether $1844$ is divisible by $2$.

It is divisible, thus, divide $1844$ by ${\color{green}2}$: $\frac{1844}{2} = {\color{red}922}$.

Determine whether $922$ is divisible by $2$.

It is divisible, thus, divide $922$ by ${\color{green}2}$: $\frac{922}{2} = {\color{red}461}$.

The prime number ${\color{green}461}$ has no other factors then $1$ and ${\color{green}461}$: $\frac{461}{461} = {\color{red}1}$.

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: $3688 = 2^{3} \cdot 461$.

The prime factorization is $3688 = 2^{3} \cdot 461$A.