Multiple Number Support
Calculate GCF for two or more integers with advanced algorithms and optimization
Euclidean Algorithm Steps
Show detailed step-by-step process using the efficient Euclidean algorithm method
Educational Explanations
Learn the mathematical principles behind GCF calculation with clear examples
Start Calculating
Enter your numbers and get instant GCF results with detailed steps
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What is the Greatest Common Factor?
Understanding GCF and its mathematical significance
The Greatest Common Factor (GCF), also known as the Greatest Common Divisor (GCD), is the largest positive integer that divides each of the given numbers without leaving a remainder.
Understanding GCF is essential for simplifying fractions, solving problems involving ratios, and finding patterns in number relationships. It's a fundamental concept in number theory and algebra.
Key Properties
Example: GCF(48, 18)
GCF = 6
Methods to Find GCF
Three effective approaches for calculating GCF
Prime Factorization
Find the prime factors of each number, then multiply the common prime factors with their lowest powers.
Euclidean Algorithm
Repeatedly divide and take remainders until the remainder is 0. The last non-zero remainder is the GCF.
Listing Factors
List all factors of each number, then find the largest factor that appears in all lists.
GCF Calculation Examples
Practice with different types of number combinations
Example 1: Two Numbers
Numbers: 24 and 36
GCF: 12
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
Example 2: Three Numbers
Numbers: 15, 25, 35
GCF: 5
Prime factorization:
15 = 3 × 5, 25 = 5², 35 = 5 × 7
Common factor: 5
Example 3: Prime Numbers
Numbers: 7 and 11
GCF: 1
Both are prime numbers
Prime numbers share no common factors except 1
Example 4: Large Numbers
Numbers: 120 and 180
GCF: 60
Using Euclidean algorithm:
180 = 120×1 + 60, 120 = 60×2 + 0
Frequently Asked Questions
Common questions about GCF calculations