# Prime factorization of $2180$

The calculator will find the prime factorization of $2180$, with steps shown.

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Find the prime factorization of $2180$.

### Solution

Start with the number $2$.

Determine whether $2180$ is divisible by $2$.

It is divisible, thus, divide $2180$ by ${\color{green}2}$: $\frac{2180}{2} = {\color{red}1090}$.

Determine whether $1090$ is divisible by $2$.

It is divisible, thus, divide $1090$ by ${\color{green}2}$: $\frac{1090}{2} = {\color{red}545}$.

Determine whether $545$ is divisible by $2$.

Since it is not divisible, move to the next prime number.

The next prime number is $3$.

Determine whether $545$ is divisible by $3$.

Since it is not divisible, move to the next prime number.

The next prime number is $5$.

Determine whether $545$ is divisible by $5$.

It is divisible, thus, divide $545$ by ${\color{green}5}$: $\frac{545}{5} = {\color{red}109}$.

The prime number ${\color{green}109}$ has no other factors then $1$ and ${\color{green}109}$: $\frac{109}{109} = {\color{red}1}$.

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: $2180 = 2^{2} \cdot 5 \cdot 109$.

The prime factorization is $2180 = 2^{2} \cdot 5 \cdot 109$A.