GCD/HCF Calculator
Find Greatest Common Divisor / Highest Common Factor
Separate numbers with commas, spaces, or semicolons
Examples:
12, 18
GCD(12, 18) = 6
24, 36, 48
GCD(24, 36, 48) = 12
17, 19
GCD(17, 19) = 1 (Co-prime)
45, 60, 75
GCD(45, 60, 75) = 15
About GCD/HCF
The Greatest Common Divisor (GCD) or Highest Common Factor (HCF)of two or more integers is the largest positive integer that divides each of the numbers without remainder.
Euclidean Algorithm
Repeated division until remainder is zero. Efficient for large numbers.
Prime Factorization
Find common prime factors and multiply them. Good for understanding concepts.
Frequently Asked Questions (FAQs)
GCD (Greatest Common Divisor) or HCF (Highest Common Factor) is the largest positive integer that divides two or more numbers without leaving a remainder.
Euclidean Algorithm uses repeated division and is efficient for large numbers. Prime Factorization finds all prime factors first, then identifies common ones.
Numbers are co-prime (or relatively prime) if their GCD is 1. Example: 15 and 28 are co-prime because GCD(15, 28) = 1.
GCD is used in simplifying fractions, scheduling repeating events, cryptography, and solving problems involving ratios and proportions.
No, GCD cannot be larger than any of the numbers. The GCD is always less than or equal to the smallest number in the set.
Methods to Calculate GCD/HCF
Euclidean Algorithm
- Divide larger number by smaller number
- Replace larger number with remainder
- Repeat until remainder is zero
- Last non-zero remainder is the GCD
Prime Factorization
- Find prime factors of each number
- Identify common prime factors
- Multiply common factors
- Result is the GCD
Tip: Use Euclidean Algorithm for efficiency with large numbers. Use Prime Factorization for better understanding of the concept.
