Greatest Common Divisor - GCD

The Greatest Common Divisor (GCD), also known as the Highest Common Factor (HCF), is the greatest number that divides a set of numbers without leaving a remainder. For example, the GCD of 4 and 6 is 2, as it divides both numbers and is the largest of all their factors.

The GCD of any two numbers is never negative or 0, and the least positive integer common to any two numbers is always 1.

Examples of GCD (Greatest Common Divisor)

Here are some examples of the GCD of Two Numbers:

12 and 18:
Divisors of 12 are 1, 2, 3, 4, 6 and 12
Divisors of 18 are 1, 2, 3, 6, 9 and 18
The common Divisors are 1, 2, 3 and 6. The greatest common divisor or GCD is 6

30 and 15:
Divisors of 30 are 1, 2, 3, 5, 15 and 30
Divisors of 15 are 1, 3, 5 and 15
The common Divisors are 1, 3, 5 and 15. The greatest common divisor or GCD is 15.

4 and 9:
Divisors of 4 are 1, 2 and 4
Divisors of 9 are 1, 3 and 9
There is only one common divisor 1. Hence GCD is 1.

GCD for Beginners

This section covers the basics of GCD, different methods to find it, its properties, and real-life uses explained simply.

• How to find GCD (Greatest Common Divisor)?
• How to find the GCD of more than 2 numbers
• Relation between GCD and LCM
• Properties of GCD
• Euclid Division Lemma
• Euclidean Algorithm
• Extended Euclidean Algorithm
• Applications of GCD in Real Life
• Tips and Tricks to Find GCD (Greatest Common Divisor)
• GCD Calculator

GCD for Aptitude Preparation

Prepare for aptitude exams with shortcut methods, solved examples, and common GCD-related questions.

• Short Tricks to Solve GCD with Solved Examples
• Interesting Facts about GCD
• HCF / GCD and LCM – Aptitude Questions & Answers

GCD Practice Questions

Practice GCD problems of varying difficulty, including MCQs to test and improve your problem-solving skills.

• GCD Practice Questions (Easy Level)
• GCD Practice Questions (Medium Level)
• GCD Practice Questions (Hard Level)
• MCQs on GCD

GCD for Programmers

Learn how to solve GCD-related problems using code, from basic programs to competitive programming challenges.

• Program for GCD of Two Numbers
• GCD of an array
• Add two fractions
• Check for Co-Prime
• Water Jug Problem
• GCD Practice Problems for Competitive Programming
• GCD Coding Problems