Question
Download Solution PDFWhat is the HCF of 7/9, 14/15 and 7/10?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDF
Concept Used:
The HCF of fractions is calculated using the formula:
HCF of fractions = HCF of numerators / LCM of denominators
Here:
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HCF of numerators = HCF(7, 14, 7)
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LCM of denominators = LCM(9, 15, 10)
Calculation:
Step 1: Find the HCF of the numerators (7, 14, 7).
The factors of 7: 1, 7
The factors of 14: 1, 2, 7, 14
Common factors = 1, 7
⇒ HCF(7, 14, 7) = 7
Step 2: Find the LCM of the denominators (9, 15, 10).
The prime factorization of 9: 32
The prime factorization of 15: 3 × 5
The prime factorization of 10: 2 × 5
LCM = Highest power of all prime factors = 2 × 32 × 5 = 90
Step 3: Calculate the HCF of the fractions:
HCF = HCF of numerators / LCM of denominators
⇒ HCF = 7 / 90
Conclusion:
∴ The HCF of 7/9, 14/15, and 7/10 is 7/90.
Last updated on Jul 1, 2025
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