mathematics Verified Precision Tool
GCD Calculator (Greatest Common Divisor)
Calculate the greatest common divisor (GCD) or highest common factor (HCF) of numbers.
Calculation Solution
GCD = 50
Euclidean Algorithm Result
Mathematical Formula
GCD(a, b) via Euclidean Algorithm
Overview & Explanation
The Greatest Common Divisor (GCD), also known as Highest Common Factor (HCF), is the largest positive integer that divides both numbers without a remainder.
How It Works
- Apply the Euclidean algorithm iteratively: GCD(a, b) = GCD(b, a mod b) until remainder is zero.
Practical Applications
- Simplifying ratios and fractions.
- Tiling rectangular areas without cutting tiles.
Worked Example: GCD of 48 and 180
Find GCD.
1
Euclidean Algorithm
180 mod 48 = 36, 48 mod 36 = 12, 36 mod 12 = 0
= 12
Frequently Asked Questions
Is HCF the same as GCD?
Yes. Highest Common Factor (HCF) and Greatest Common Divisor (GCD) are identical concepts.
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