Is 25/36 in simplest form if not what is it in simplest form
The Correct Answer and Explanation is :
To determine if the fraction ( \frac{25}{36} ) is in its simplest form, we need to check if the numerator (25) and the denominator (36) have any common factors other than 1. A fraction is in simplest form when the numerator and the denominator are coprime, meaning their greatest common divisor (GCD) is 1.
Step 1: Find the Prime Factorization
- Numerator (25):
- The prime factorization of 25 is ( 5 \times 5 ) or ( 5^2 ).
- Denominator (36):
- The prime factorization of 36 is ( 2 \times 2 \times 3 \times 3 ) or ( 2^2 \times 3^2 ).
Step 2: Identify Common Factors
Next, we can compare the prime factors of both the numerator and denominator:
- Factors of 25: ( 5 )
- Factors of 36: ( 2 ) and ( 3 )
Since the factors of 25 (which is ( 5^2 )) do not overlap with the factors of 36 (which are ( 2^2 \times 3^2 )), the only common factor is 1.
Step 3: Conclusion
Since the GCD of 25 and 36 is 1, we can conclude that ( \frac{25}{36} ) is already in its simplest form. There are no common factors that can simplify the fraction further.
Final Answer
Thus, the fraction ( \frac{25}{36} ) is indeed in simplest form and cannot be reduced any further. This means that it can be used as is in calculations and representations without any further simplification needed.
Summary
In summary, to determine if a fraction is in simplest form, check for common factors between the numerator and denominator. In the case of ( \frac{25}{36} ), the lack of common prime factors confirms that it is simplified to its lowest terms.