GCF, or the greatest common factor, is a mathematical term used to represent the largest number or common divisor that divides into two or more given numbers without leaving a remainder. It is also commonly referred to as the greatest common divisor (GCD).
To determine the GCF of a set of numbers, one must identify all the factors or divisors of each number and find the one that is common to all. The GCF can be calculated for any two or more integers, either positive or negative.
For example, consider the numbers 12 and 18. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 18 are 1, 2, 3, 6, 9, and 18. The largest number that divides both 12 and 18 without remainder is 6. Therefore, the GCF of 12 and 18 is 6.
The GCF is a fundamental concept in various mathematical operations, including simplifying fractions, finding equivalent fractions, and solving problems involving factors. It is often used in algebraic expressions to simplify equations and expressions.
In summary, the GCF is the largest common factor or divisor shared by two or more given numbers, obtained by identifying the factors and selecting the highest common factor. It is an essential mathematical tool used in various applications, aiding in simplifying problems and calculations.
