# Prime factorization of $1975$

The calculator will find the prime factorization of $1975$, with steps shown.

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Find the prime factorization of $1975$.

### Solution

Start with the number $2$.

Determine whether $1975$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1975$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $1975$ is divisible by $5$.

It is divisible, thus, divide $1975$ by ${\color{green}5}$: $\frac{1975}{5} = {\color{red}395}$.

Determine whether $395$ is divisible by $5$.

It is divisible, thus, divide $395$ by ${\color{green}5}$: $\frac{395}{5} = {\color{red}79}$.

The prime number ${\color{green}79}$ has no other factors then $1$ and ${\color{green}79}$: $\frac{79}{79} = {\color{red}1}$.

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: $1975 = 5^{2} \cdot 79$.

The prime factorization is $1975 = 5^{2} \cdot 79$A.