The full form of GCD is Greatest Common Divisor.
The Greatest Common Divisor (GCD), also known as the Highest Common Factor (HCF), is the largest positive integer that divides two or more integers without leaving a remainder. It's a fundamental concept in number theory.
Here's a breakdown:
- Greatest: Refers to the largest number that satisfies the condition.
- Common: Indicates that the number is a factor of all the given integers.
- Divisor: A number that divides another number evenly (without a remainder).
Example:
Consider the numbers 12 and 18.
- The divisors of 12 are: 1, 2, 3, 4, 6, and 12.
- The divisors of 18 are: 1, 2, 3, 6, 9, and 18.
The common divisors of 12 and 18 are: 1, 2, 3, and 6.
The greatest of these common divisors is 6. Therefore, the GCD of 12 and 18 is 6.
