HCF (GCD) Calculator
Find the Highest Common Factor — also known as Greatest Common Divisor — with step-by-step Euclidean algorithm working.
HCF Calculator – Highest Common Factor Explained
The Highest Common Factor (HCF), also called Greatest Common Divisor (GCD), is the largest number that divides two or more integers without leaving a remainder. It is a cornerstone of number theory and essential for simplifying fractions, solving ratio problems, and many real-world tasks.
Methods to Find HCF
Euclidean Algorithm
The most efficient method. Repeatedly divide the larger number by the smaller one and replace with the remainder until the remainder is zero. The last non-zero remainder is the HCF. Example: HCF(48, 18): 48 = 2×18 + 12 → 18 = 1×12 + 6 → 12 = 2×6 + 0 → HCF = 6.
Prime Factorization
Factor each number into primes, then identify common prime factors and take the lowest power of each. The product of these is the HCF. Example: HCF(12, 8): 12 = 2²×3, 8 = 2³ → HCF = 2² = 4.
Real-World Applications
- Simplifying fractions: Divide numerator and denominator by their HCF.
- Tiling/cutting: Find the largest tile that fits perfectly in two dimensions.
- Ratio reduction: Simplify ratios to their lowest terms using HCF.
- Equal distribution: Find the largest group size that evenly divides multiple quantities.
Relationship Between HCF and LCM
For any two numbers a and b: HCF(a,b) × LCM(a,b) = a × b. This useful identity lets you find one if you know the other.
Frequently Asked Questions
What is the HCF of co-prime numbers?
Co-prime (or relatively prime) numbers share no common factor other than 1. Their HCF is always 1. For example, HCF(9, 16) = 1.
What is the HCF of a number and itself?
The HCF of any number with itself is the number itself. HCF(7, 7) = 7.