HCF / GCD Calculator - Highest Common Factor HCF Calculator
Enter two or more numbers to instantly find their Highest Common Factor (GCD).
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Prime Factorization
24 = 2³ × 3
36 = 2² × 3²
HCF = 2² × 3 = 12
HCF / GCD Calculator - Guide
What is HCF / GCD?
The Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), is the largest positive integer that divides two or more numbers without leaving a remainder. For example, the HCF of 12 and 18 is 6 because 6 is the largest number that divides both evenly.
How to Find HCF
1. Prime Factorization Method
Find prime factors of each number, then take the lowest power of each common prime and multiply them.
2. Euclidean Algorithm
Divide the larger number by the smaller; replace the larger with the remainder. Repeat until remainder is 0. The last non-zero value is the HCF.
3. Division Method
List all factors of each number and pick the largest common one.
Examples
- HCF(12, 18): 12 = 2² × 3, 18 = 2 × 3² → HCF = 2 × 3 = 6
- HCF(24, 36): 24 = 2³ × 3, 36 = 2² × 3² → HCF = 2² × 3 = 12
- HCF(7, 13): Both are prime → HCF = 1 (coprime)
- HCF(48, 60, 72): Common factors: 2² × 3 = 12
Common Uses of HCF
- Simplifying fractions: Divide numerator and denominator by their HCF to get the simplest form.
- Distributing items: Split items into the largest possible equal groups.
- Tiling: Find the largest square tile that can perfectly cover a rectangular floor.
- Number theory: Determine if numbers are coprime (HCF = 1).
How This Calculator Works
- Enter numbers: Type two or more positive integers separated by commas or spaces.
- Instant results: The HCF, LCM, product, and coprime status update in real time.
- Step-by-step: View the prime factorization breakdown for each number.