Simplifying the Fraction: 625/256
When working with fractions, it's often essential to simplify them to their lowest form. This process involves finding the greatest common divisor (GCD) of the numerator and denominator and dividing both numbers by the GCD. In this article, we'll explore how to simplify the fraction 625/256.
Finding the Greatest Common Divisor (GCD)
To simplify the fraction 625/256, we need to find the GCD of 625 and 256. The GCD is the largest number that divides both numbers without leaving a remainder. We can use the following steps to find the GCD:
- List the factors of 625: 1, 5, 25, 125, 625
- List the factors of 256: 1, 2, 4, 8, 16, 32, 64, 128, 256
- Identify the common factors: 1
Since the only common factor is 1, the GCD of 625 and 256 is 1.
Simplifying the Fraction
Now that we know the GCD is 1, we can simplify the fraction 625/256 by dividing both the numerator and denominator by 1.
625 ÷ 1 = 625 256 ÷ 1 = 256
The simplified fraction is still 625/256.
Conclusion
In conclusion, the fraction 625/256 is already in its lowest form. There is no way to simplify it further, as the GCD of the numerator and denominator is 1. Therefore, the answer is:
625/256
