Greatest Common Factor Calculator
Find the greatest common factor (GCF) of two or more numbers with step-by-step calculations and explanations
GCF Calculator
Methods to Find GCF
Euclidean Algorithm:
GCF(a,b) = GCF(b, a mod b)
Example: GCF(48, 18) = GCF(18, 12) = GCF(12, 6) = GCF(6, 0) = 6
Prime Factorization:
Find common prime factors with smallest power
Example: 24 = 2³ × 3, 36 = 2² × 3², GCF = 2² × 3 = 12
Results
Step 1: Finding GCF of 24 and 36
Using the Euclidean algorithm:
- Swap numbers so larger number comes first: 36 and 24
- GCF(36, 24) = GCF(24, 12)
- GCF(24, 12) = GCF(12, 0)
- Since the remainder is now 0, GCF = 12
The greatest common factor of 24, 36 is 12.
Common GCF Values
The greatest common factor (GCF) is useful for simplifying fractions, factoring algebraic expressions, and solving various mathematical problems.
Key Features
Multiple Numbers
Calculate the GCF of two or more numbers with our easy-to-use interface that handles multiple inputs.
Multiple Methods
Choose between Euclidean algorithm or prime factorization methods to calculate the GCF with step-by-step workings.
Educational Tool
Learn about GCF calculation methods with detailed explanations of each step in the calculation process.
Understanding Greatest Common Factor
Learn about GCF, its applications, and calculation methods
What is the Greatest Common Factor (GCF)?
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 two or more integers without a remainder. In other words, it's the largest factor that the numbers share in common.
Applications of GCF
Simplifying Fractions:
Reduce fractions to lowest terms by dividing both numerator and denominator by their GCF.
Factoring Expressions:
Factor out the GCF from algebraic expressions and polynomials.
Practical Applications:
Determine the largest equal portions into which different quantities can be divided.
Methods to Calculate GCF
Euclidean Algorithm
An efficient method that uses repeated division to find the GCF.
Steps:
- Divide the larger number by the smaller number
- Replace the larger number with the smaller number
- Replace the smaller number with the remainder
- Repeat until the remainder is 0
- The last non-zero remainder is the GCF
GCF(48, 18) = GCF(18, 12) = GCF(12, 6) = GCF(6, 0) = 6
Prime Factorization
Breaking down numbers into their prime factors to find common factors.
Steps:
- Find prime factorization of each number
- Identify common prime factors
- Take each common prime factor to the smallest power it appears
- Multiply these factors to get the GCF
24 = 2³ × 3, 36 = 2² × 3², GCF = 2² × 3 = 12
Listing Factors Method
A straightforward method suitable for smaller numbers.
Steps:
- List all factors of each number
- Identify common factors
- Find the largest common factor
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Common factors: 1, 2, 3, 4, 6, 12
GCF = 12
Did You Know?
The concept of finding the greatest common divisor (GCD) or greatest common factor (GCF) dates back to Euclid's Elements (around 300 BCE). The Euclidean algorithm is one of the oldest algorithms still used today. In modern computing, GCD calculations are fundamental for many applications, including cryptography, where they play a role in algorithms like RSA for public key encryption.
Frequently Asked Questions
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