GCF of 12 and 18
Both numbers share several factors, but 6 is the largest one they have in common.
Factors of 12: 1, 2, 3, 4, 6, 12; Factors of 18: 1, 2, 3, 6, 9, 18
Result: GCF(12, 18) = 6
Greatest Common Factor Calculator
Use this calculator to find the greatest common factor (GCF) of two or more numbers. Get step-by-step solutions and understand how GCF is calculated.
Greatest Common Factor Calculator
Enter two or more numbers separated by commas, then click Calculate to find their greatest common factor (GCF).
Result
What is the Greatest Common Factor (GCF)?
The Greatest Common Factor (GCF), also known as the Greatest Common Divisor (GCD), is the largest positive integer that divides two or more numbers without a remainder.
For example, the GCF of 12 and 18 is 6, because 6 is the largest number that divides both 12 and 18 evenly.
Methods to Find the GCF
Euclidean Algorithm
This method uses repeated division to find the GCF. It's based on the principle that if a and b are two positive integers, then GCF(a,b) = GCF(b, a mod b).
Example: To find GCF(48, 18) 1. Divide: 48 ÷ 18 = 2 remainder 12 2. Replace: GCF(48, 18) = GCF(18, 12) 3. Divide: 18 ÷ 12 = 1 remainder 6 4. Replace: GCF(18, 12) = GCF(12, 6) 5. Divide: 12 ÷ 6 = 2 remainder 0 6. When remainder is 0, the divisor (6) is the GCF Therefore, GCF(48, 18) = 6
Prime Factorization Method
This method involves finding the prime factorization of each number, then multiplying the common prime factors with their lowest powers.
Example: To find GCF(12, 18) 1. Prime factorization: 12 = 2² × 3, 18 = 2 × 3² 2. Common factors: 2¹ and 3¹ (lowest powers) 3. Multiply them: 2¹ × 3¹ = 2 × 3 = 6 Therefore, GCF(12, 18) = 6
Applications of GCF
- Simplifying fractions to their lowest terms
- Finding the largest possible size for equal groups or portions
- Solving problems in number theory and cryptography
- Reducing measurements to their simplest form in engineering and design
How to Use This Calculator
- Enter two or more positive integers separated by commas in the input field.
- Click the 'Calculate' button to find the GCF.
- View the result and the step-by-step solution explaining how the GCF was calculated.
- Click 'Clear' to reset the calculator and perform a new calculation.
Tip: the GCF is especially useful for simplifying fractions and grouping items into the largest equal sets.
GCF Examples
GCF of 24 and 36
A larger shared factor appears because both numbers are divisible by 12.
24 = 2³ × 3, 36 = 2² × 3²
Result: GCF(24, 36) = 12
GCF of Three Numbers
The calculator can also compare more than two integers at once.
GCF(18, 30, 42)
Result: 6
Using GCF to Simplify Fractions
If the numerator and denominator share a GCF, divide both by that value.
24/36 ÷ 12/12
Result: 24/36 = 2/3
GCF Calculator FAQ
What is the greatest common factor?
The greatest common factor is the largest positive integer that divides each number in a set without leaving a remainder.
Is GCF the same as GCD?
Yes. GCF, greatest common divisor, and highest common factor all refer to the same concept.
Why is GCF useful for fractions?
The GCF helps simplify fractions by identifying the largest number that can divide both the numerator and denominator.
Can the calculator find the GCF of more than two numbers?
Yes. Enter multiple positive integers separated by commas, and the calculator will determine their shared greatest common factor.