workspaces

GCF Calculator

Find the Greatest Common Factor (GCF) of two or more numbers. Also known as GCD or HCF.

help_outline

How to Use

expand_more

Enter two or more whole numbers in the input field
Separate numbers with commas or spaces (e.g., "18, 27" or "8 12 20")
Click "Calculate" or press Enter
View the GCF along with the step-by-step factorization solution

info

What is GCF Calculator?

expand_more

The Greatest Common Factor (GCF), also known as the Greatest Common Divisor (GCD) or Highest Common Factor (HCF), is the largest positive integer that divides each of the given numbers without leaving a remainder.

For example, the GCF of 18 and 27 is 9, because 9 is the largest number that divides both 18 and 27 evenly (18 ÷ 9 = 2 and 27 ÷ 9 = 3).

The GCF is commonly used in simplifying fractions, finding common denominators, and solving various mathematical problems involving divisibility.

functions

Formula

expand_more

Method 1: Factorization

List all factors of each number, find the common factors, and select the greatest one.

Method 2: Euclidean Algorithm

GCD(a, b) = GCD(b, a mod b), repeat until remainder is 0.

Method 3: Prime Factorization

Find the prime factorization of each number, then multiply the common prime factors.

lightbulb

Examples

expand_more

Example 1: GCF(18, 27)

Factors of 18: 1, 2, 3, 6, 9, 18

Factors of 27: 1, 3, 9, 27

Common factors: 1, 3, 9

GCF = 9

Example 2: GCF(8, 12, 20)

Factors of 8: 1, 2, 4, 8

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of 20: 1, 2, 4, 5, 10, 20

Common factors: 1, 2, 4

GCF = 4

quiz

FAQ

expand_more

What is the difference between GCF, GCD, and HCF?expand_more

GCF (Greatest Common Factor), GCD (Greatest Common Divisor), and HCF (Highest Common Factor) all refer to the same concept - the largest positive integer that divides all given numbers without a remainder. Different regions and textbooks use different terms.

What is the GCF of two prime numbers?expand_more

The GCF of two different prime numbers is always 1, because prime numbers have no common factors other than 1. For example, GCF(7, 11) = 1.

How is GCF used to simplify fractions?expand_more

To simplify a fraction, divide both the numerator and denominator by their GCF. For example, to simplify 18/27: GCF(18, 27) = 9, so 18/27 = (18÷9)/(27÷9) = 2/3.

What is GCF(0, n)?expand_more

The GCF of 0 and any non-zero number n is |n| (the absolute value of n). This is because every integer divides 0, so the GCF is determined by the non-zero number.