Find the H.C.F. of 9⁄10, 12⁄25, 18⁄35, and 21⁄40.

Given data

• Fractions: 9⁄10, 12⁄25, 18⁄35, 21⁄40

Concept / Approach

• H.C.F. of fractions = HCF of numerators divided by LCM of denominators.

Step-by-step

HCF of numerators HCF(9, 12, 18, 21) = 3LCM of denominators LCM(10, 25, 35, 40)Prime factors: 10 = 2 × 5; 25 = 5^2; 35 = 5 × 7; 40 = 2^3 × 5LCM = 2^3 × 5^2 × 7 = 8 × 25 × 7 = 1400Therefore H.C.F. = 3⁄1400 = 3⁄1400

Common pitfalls

• Using LCM of numerators by mistake, which is for LCM of fractions, not HCF.

Final Answer

3⁄1400