# Prime factorization of $2075$

The calculator will find the prime factorization of $2075$, with steps shown.

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Find the prime factorization of $2075$.

### Solution

Start with the number $2$.

Determine whether $2075$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2075$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $2075$ is divisible by $5$.

It is divisible, thus, divide $2075$ by ${\color{green}5}$: $\frac{2075}{5} = {\color{red}415}$.

Determine whether $415$ is divisible by $5$.

It is divisible, thus, divide $415$ by ${\color{green}5}$: $\frac{415}{5} = {\color{red}83}$.

The prime number ${\color{green}83}$ has no other factors then $1$ and ${\color{green}83}$: $\frac{83}{83} = {\color{red}1}$.

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: $2075 = 5^{2} \cdot 83$.

The prime factorization is $2075 = 5^{2} \cdot 83$A.