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What is GCF (Greatest Common Factor)?

The Greatest Common Factor (GCF), also called Greatest Common Divisor (GCD), is the largest number that divides evenly into two or more numbers.

For example, GCF(24, 36) = 12, because 12 is the largest number that divides both 24 and 36.

GCF is calculated using the Euclidean algorithm, one of the oldest algorithms in mathematics (dating back to 300 BC).

Methods to find GCF:

Euclidean algorithm: Repeatedly divide and take remainders until reaching 0
Prime factorization: Find prime factors of each number, multiply the common ones
Listing factors: List all factors of each number and find the largest shared one

This calculator uses the Euclidean algorithm for efficiency.

GCF is used to simplify fractions (divide numerator and denominator by GCF), solve distribution problems, and find common measurements.

For example, to simplify 24/36: GCF(24,36) = 12, so 24/36 = 2/3.

What is GCF of 24 and 36?

GCF(24, 36) = 12. The number 12 is the largest factor common to both 24 and 36.

Is GCF the same as GCD?

Yes. GCF (Greatest Common Factor), GCD (Greatest Common Divisor), and HCF (Highest Common Factor) all refer to the same concept.

What if GCF is 1?

If GCF of two numbers is 1, they are called 'coprime' or 'relatively prime' — they share no common factors other than 1. Пример: GCF(7, 9) = 1.