GCF Calculator

Find the Greatest Common Factor (GCF) / Greatest Common Divisor (GCD) of two or more numbers. Get step-by-step solutions.

Greatest Common Factor (GCF)

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Input Numbers

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Summary

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Step-by-Step Solution

Enter numbers and click "Calculate" to see the step-by-step solution.

What is GCF?

The Greatest Common Factor (GCF) is the largest positive integer that divides each of the given numbers without a remainder. It is also known as:

  • Greatest Common Divisor (GCD)
  • Highest Common Factor (HCF)
  • Greatest Common Denominator (GCD)

How to Find GCF

  • Listing Factors: List all factors of each number
  • Prime Factorization: Find common prime factors
  • Euclidean Algorithm: Repeated division method

Common Examples

  • GCF of 12 and 18: 6
  • GCF of 24 and 36: 12
  • GCF of 8, 12, and 20: 4
  • GCF of 15 and 28: 1 (coprime)

Frequently Asked Questions

What is the Greatest Common Factor (GCF)?

The Greatest Common Factor (GCF) is the largest number that divides two or more numbers evenly (without remainder). For example, the GCF of 12 and 18 is 6 because 6 is the largest number that divides both 12 and 18.

How do I calculate GCF using the Euclidean Algorithm?

Step 1: Divide the larger number by the smaller number

Step 2: Replace the larger number with the remainder

Step 3: Repeat until remainder is 0

Step 4: The last non-zero remainder is the GCF

What is the GCF of 24 and 36?

The GCF of 24 and 36 is 12. Factors of 24: 1,2,3,4,6,8,12,24. Factors of 36: 1,2,3,4,6,9,12,18,36. The largest common factor is 12.

What is the difference between GCF and LCM?

GCF (Greatest Common Factor) is the largest number that divides all given numbers. LCM (Least Common Multiple) is the smallest number that is a multiple of all given numbers. For 4 and 6: GCF = 2, LCM = 12.

What if the numbers have no common factors?

If numbers have no common factors other than 1, they are called coprime or relatively prime. The GCF is 1. For example, GCF of 15 and 28 is 1.