HCF of several fractions Find the highest common factor (HCF) of the fractions 1/2, 2/3, 3/4, and 4/5 using the rule HCF = HCF(numerators) / LCM(denominators).

Introduction / Context:
For fractions, the HCF is not found by simple integer gcd on numerators and denominators together. Instead, apply the special rule: HCF of fractions equals HCF of numerators divided by LCM of denominators.

Given Data / Assumptions:

• Fractions: 1/2, 2/3, 3/4, 4/5.
• All positive.

Concept / Approach:
Compute HCF(1, 2, 3, 4) and LCM(2, 3, 4, 5), then divide.

Step-by-Step Solution:
HCF of numerators: gcd(1, 2, 3, 4) = 1.LCM of denominators: LCM(2, 3, 4, 5) = 60.Therefore HCF of fractions = 1 / 60.

Verification / Alternative check:
Each given fraction divided by 1/60 yields an integer: (1/2) ÷ (1/60) = 30; (2/3) ÷ (1/60) = 40; (3/4) ÷ (1/60) = 45; (4/5) ÷ (1/60) = 48.

Why Other Options Are Wrong:
1 and 12 are integers, not common fractional divisors for all; 4/5 is larger than most inputs; 1/30 is a common divisor but not the greatest by the rule.

Common Pitfalls:
Mixing up rules for HCF vs LCM on fractions; canceling across numbers incorrectly.

Final Answer:
1/60