Please provide numbers separated by a comma "," and click the "Calculate" button to find the GCF.
In mathematics, the Greatest Common Factor (also known as the Greatest Common Divisor (GCD) or Highest Common Factor (HCF)) of two or more non-zero integers is the largest positive integer that divides all of them without leaving a remainder.
For example, consider 48 and 64:
The common factors are 1, 2, 4, 8, and 16. The largest among them is 16, meaning GCF(48, 64) = 16.
Break each number into prime powers. The GCF is the product of only the prime factors that are common to all numbers, raised to their lowest exponent:
Repeatedly apply division modulo: gcd(a, b) = gcd(b, a mod b). The last non-zero remainder is the GCF:
List every positive divisor for each integer, determine their common intersection, and identify the highest element.
Dividing both the numerator and denominator by their GCF reduces any fraction to its simplest irreducible form in one step (e.g. 48/64 ÷ 16/16 = 3/4).
Distributing distinct quantities of items (e.g. 48 apples and 64 oranges) into identical gift bags with zero leftovers requires calculating the GCF.
Finding the largest square tile size that can tile a rectangular floor (e.g. 48m × 64m) without cutting any tiles uses the GCF.
Two numbers are coprime (mutually prime or relatively prime) if their greatest common factor is 1 (e.g. GCF(15, 28) = 1). They share no common prime factors.
For any non-zero integer a, GCF(a, 0) = |a|, because every non-zero integer divides 0 without remainder (0 = 0 × a). However, GCF(0, 0) is undefined.
Yes. Greatest Common Factor (GCF), Greatest Common Divisor (GCD), and Highest Common Factor (HCF) are completely synonymous mathematical terms.