Greatest Common Factor Calculator
Find the GCD of multiple numbers with detailed solutions
Greatest Common Factor Calculator
Calculate the greatest common factor (GCD) of multiple numbers. Enter numbers separated by commas to find the largest positive integer that divides all of them.
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đ Understanding Greatest Common Factor (GCD)
What is GCD?
In mathematics, the greatest common factor (GCF), also known as the greatest common divisor, is the largest positive integer by which all given integers can be divided.
Prime Factorization
One method involves computing the prime factorizations of each integer, determining which factors they have in common, and multiplying these factors.
Euclidean Algorithm
The Euclidean algorithm is a more efficient method for finding GCD, especially for larger numbers. It uses division and the principle that GCD can also divide their difference.
Prime Factorization Method
There are multiple ways to find the greatest common factor of given integers. One of these involves computing the prime factorizations of each integer, determining which factors they have in common, and multiplying these factors to find the GCD.
Euclidean Algorithm
The Euclidean algorithm uses a division algorithm combined with the observation that the GCD of two integers can also divide their difference. This method is far more efficient than prime factorization for larger numbers.
Continue this process until one number becomes zero. The GCD is the non-zero remainder.