# Prime factorization of $2176$

The calculator will find the prime factorization of $2176$, with steps shown.

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Find the prime factorization of $2176$.

### Solution

Start with the number $2$.

Determine whether $2176$ is divisible by $2$.

It is divisible, thus, divide $2176$ by ${\color{green}2}$: $\frac{2176}{2} = {\color{red}1088}$.

Determine whether $1088$ is divisible by $2$.

It is divisible, thus, divide $1088$ by ${\color{green}2}$: $\frac{1088}{2} = {\color{red}544}$.

Determine whether $544$ is divisible by $2$.

It is divisible, thus, divide $544$ by ${\color{green}2}$: $\frac{544}{2} = {\color{red}272}$.

Determine whether $272$ is divisible by $2$.

It is divisible, thus, divide $272$ by ${\color{green}2}$: $\frac{272}{2} = {\color{red}136}$.

Determine whether $136$ is divisible by $2$.

It is divisible, thus, divide $136$ by ${\color{green}2}$: $\frac{136}{2} = {\color{red}68}$.

Determine whether $68$ is divisible by $2$.

It is divisible, thus, divide $68$ by ${\color{green}2}$: $\frac{68}{2} = {\color{red}34}$.

Determine whether $34$ is divisible by $2$.

It is divisible, thus, divide $34$ by ${\color{green}2}$: $\frac{34}{2} = {\color{red}17}$.

The prime number ${\color{green}17}$ has no other factors then $1$ and ${\color{green}17}$: $\frac{17}{17} = {\color{red}1}$.

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: $2176 = 2^{7} \cdot 17$.

The prime factorization is $2176 = 2^{7} \cdot 17$A.