# Prime factorization of $1636$

The calculator will find the prime factorization of $1636$, with steps shown.

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Find the prime factorization of $1636$.

### Solution

Start with the number $2$.

Determine whether $1636$ is divisible by $2$.

It is divisible, thus, divide $1636$ by ${\color{green}2}$: $\frac{1636}{2} = {\color{red}818}$.

Determine whether $818$ is divisible by $2$.

It is divisible, thus, divide $818$ by ${\color{green}2}$: $\frac{818}{2} = {\color{red}409}$.

The prime number ${\color{green}409}$ has no other factors then $1$ and ${\color{green}409}$: $\frac{409}{409} = {\color{red}1}$.

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: $1636 = 2^{2} \cdot 409$.

The prime factorization is $1636 = 2^{2} \cdot 409$A.