hcf
Master HCF
Learn the secrets of rapid mental computation used in competitive exams. These strategies will help you bypass traditional paper-and-pencil methods.
➕ Addition ➖ Subtraction ✖️ Multiplication ➗ Division x² Squaring xⁿ Exponentiation √ nth Root % Percentage △ Pythagorean Triples lcm LCM hcf HCF
hcf
★ Euclidean Algorithm
HCF(a,b) = HCF(b, a mod b). Repeatedly take the remainder until it is 0. The last non-zero value is the HCF.
Example
HCF(48,18): 48 mod 18=12, 18 mod 12=6, 12 mod 6=0 → HCF=6 hcf
★ List common factors
List all factors of both numbers and find the largest they share.
Example
HCF(12,8): factors of 12={1,2,3,4,6,12}, of 8={1,2,4,8}. Largest common = 4 hcf
★ Prime factorisation method
Break both numbers into prime factors. Take the lowest power of each prime that appears in BOTH.
Example
HCF(36,48): 36=2²×3², 48=2⁴×3. Take 2²×3 = 12 hcf
★ HCF × LCM = a × b
A key identity: HCF(a,b) × LCM(a,b) = a × b. Use it to find HCF if LCM is known.
Example
a=6, b=10, LCM=30. HCF = (6×10)/30 = 2 hcf
★ Subtract method for close numbers
HCF(a,b) = HCF(a−b, b) when a > b. Useful when numbers are close together.
Example
HCF(99, 96): HCF(3, 96)=HCF(3, 0)=3 🧠 Practice
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