The greatest common divisor (GCD) of two or more integers, at least one of which is non-zero, is the largest positive integer that divides each of the integers in that set without leaving a remainder. Also known as the highest common factor (HCF), the greatest common factor or the highest common divisor, it is the largest proper divisorNumber that when divided into another number leaves no remainder. of every member across that set of integers.[1]
The GCD is generally expressed mathematically in the form gcd(a, b) = d, as in gcd(8, 12) = 4.
Two numbers are considered to be relatively prime, or coprime, if their greatest common divisor is 1. For example, 9 and 28 are coprime, despite neither being a prime numberAny positive integer greater than zero that has only two proper divisors, 1 and the number itself. Thus the lowest prime number is 2, which is also the only even prime. .[1]
Applications
Reducing fractions
The greatest common divisor can be used to reduce fractions to their lowest terms. For example, gcd(42, 56) = 14, so
