GCF Calculator – Greatest Common Factor
Calculate the Greatest Common Factor (GCF/GCD) of two or more numbers. Also known as Greatest Common Divisor. Free math calculator. Get instant results now.
GCF (Yếu tố chung lớn nhất) là gì?
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).
Cách tìm GCF
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.
Ứng dụng GCF
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.
Frequently Asked Questions
GCF của 24 và 36 là gì?
GCF(24, 36) = 12. The number 12 is the largest factor common to both 24 and 36.
GCF có giống GCD không?
Yes. GCF (Greatest Common Factor), GCD (Greatest Common Divisor), and HCF (Highest Common Factor) all refer to the same concept.
Nếu GCF là 1 thì sao?
If GCF of two numbers is 1, they are called 'coprime' or 'relatively prime' — they share no common factors other than 1. Example: GCF(7, 9) = 1.