Greatest Common Factor (GFC) Calculator
Understanding the Greatest Common Factor (GCF)
The Greatest Common Factor (GCF), also known as the Greatest Common Divisor (GCD), is the largest number that divides two or more integers without leaving a remainder. Understanding the GCF is essential in solving problems in mathematics, such as simplifying fractions, factoring polynomials, and more.
What is the GCF?
The GCF of two or more numbers is the greatest number that is a factor of each number in the group.
For example:
- The GCF of 12 and 18 is 6.
- The GCF of 24, 36, and 48 is 12.
How to Calculate GCF Manually
There are three common methods:
Listing Factors
- Write all factors of each number.
- Identify the largest factor that appears in all lists.
- Example: For 12 (1, 2, 3, 4, 6, 12) and 18 (1, 2, 3, 6, 9, 18), the GCF is 6.
Prime Factorization
- Break each number into its prime factors.
- Multiply the common prime factors.
- Example: For 12 (2² × 3) and 18 (2 × 3²), the common factors are 2 and 3, so GCF = 2 × 3 = 6.
Division Method
- Divide the larger number by the smaller number.
- Continue dividing the remainder into the divisor until the remainder is zero.
- The last divisor is the GCF.