To simplify the fraction [tex]\(\frac{32}{3125}\)[/tex], we need to follow these steps:
1. Identify the Greatest Common Divisor (GCD):
The GCD is the largest number that divides both the numerator and the denominator without any remainder. In this case, the GCD of 32 and 3125 is 1. This means that there are no common factors between the numerator and the denominator other than 1.
2. Divide the numerator and the denominator by the GCD:
Since the GCD is 1, dividing both the numerator and the denominator by 1 does not change their values.
[tex]\[
\text{Simplified numerator} = \frac{32}{1} = 32
\][/tex]
[tex]\[
\text{Simplified denominator} = \frac{3125}{1} = 3125
\][/tex]
3. Express the simplified fraction:
Since we have found that the GCD is 1, the fraction is already in its simplest form. Therefore, [tex]\(\frac{32}{3125}\)[/tex] is already simplified and cannot be reduced further.
Thus, the simplified form of the fraction [tex]\(\frac{32}{3125}\)[/tex] is:
[tex]\[
\frac{32}{3125}
\][/tex]
In summary, the greatest common divisor (GCD) of 32 and 3125 is 1, so the fraction [tex]\(\frac{32}{3125}\)[/tex] cannot be simplified further and its simplest form is [tex]\(\boxed{\frac{32}{3125}}\)[/tex].
