# Prime factorization of $3125$

The calculator will find the prime factorization of $3125$, with steps shown.

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Find the prime factorization of $3125$.

### Solution

Start with the number $2$.

Determine whether $3125$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $3125$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $3125$ is divisible by $5$.

It is divisible, thus, divide $3125$ by ${\color{green}5}$: $\frac{3125}{5} = {\color{red}625}$.

Determine whether $625$ is divisible by $5$.

It is divisible, thus, divide $625$ by ${\color{green}5}$: $\frac{625}{5} = {\color{red}125}$.

Determine whether $125$ is divisible by $5$.

It is divisible, thus, divide $125$ by ${\color{green}5}$: $\frac{125}{5} = {\color{red}25}$.

Determine whether $25$ is divisible by $5$.

It is divisible, thus, divide $25$ by ${\color{green}5}$: $\frac{25}{5} = {\color{red}5}$.

The prime number ${\color{green}5}$ has no other factors then $1$ and ${\color{green}5}$: $\frac{5}{5} = {\color{red}1}$.

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: $3125 = 5^{5}$.

The prime factorization is $3125 = 5^{5}$A.