# Prime factorization of $1780$

The calculator will find the prime factorization of $1780$, with steps shown.

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Find the prime factorization of $1780$.

### Solution

Start with the number $2$.

Determine whether $1780$ is divisible by $2$.

It is divisible, thus, divide $1780$ by ${\color{green}2}$: $\frac{1780}{2} = {\color{red}890}$.

Determine whether $890$ is divisible by $2$.

It is divisible, thus, divide $890$ by ${\color{green}2}$: $\frac{890}{2} = {\color{red}445}$.

Determine whether $445$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $445$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $445$ is divisible by $5$.

It is divisible, thus, divide $445$ by ${\color{green}5}$: $\frac{445}{5} = {\color{red}89}$.

The prime number ${\color{green}89}$ has no other factors then $1$ and ${\color{green}89}$: $\frac{89}{89} = {\color{red}1}$.

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: $1780 = 2^{2} \cdot 5 \cdot 89$.

The prime factorization is $1780 = 2^{2} \cdot 5 \cdot 89$A.