What is GCD and why is it important for rational numbers?
GeneralClass 12AllAnswered 27 Mar 2026
Answer
GCD (Greatest Common Divisor) is the largest positive integer that divides both numbers without remainder.
Importance:
- Used to reduce fractions to standard form
- Helps identify if two fractions are equivalent
- Essential for simplifying rational number operations
Example: Find GCD of 24 and 36
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Common factors: 1, 2, 3, 4, 6, 12
- GCD = 12
Therefore, 24/36 = (24÷12)/(36÷12) = 2/3
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