Answer:
In mathematics, the GCF of two or more non-zero integers, x & y, is the greatest positive integer m, which divides both, x & y. The Greatest Common Factor is commonly known as GCF. Here, Greatest can be replaced with Highest and Factor can be replaced with Divisor. So Greatest Common Factor is also known as:
Highest Common Divisor (HCD)
Highest Common Factor (HCF)
Greatest Common Divisor (GCD)
GCF is used almost all the time with fractions, which are used a lot in everyday life. In order to simplify a fraction or a ratio, you can find the GCF of the denominator and numerator and get the required reduced form. Also, if we look around, the arrangement of something into rows and columns, distribution and grouping, all this require the understanding of GCF.
What is Greatest Common Factor (GCF)?
The GCF (Greatest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers. The GCF of two natural numbers x and y is the largest possible number that divides both x and y. To calculate GCF, there are three common ways- division, multiplication, and prime factorization.
Example: Let us find the greatest common factor of 18 and 27.
Solution:
First, we list the factors of 18 and 27 and then we find out the common factors.
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 27: 1, 3, 9, 27
The common factors of 18 and 27 are 1,3, and 9. Among these numbers, 9 is the greatest (largest) number. Thus, the GCF of 18 and 27 is 9. This is written as: GCF(18 , 27) = 9.
A factor of a number is its divisor as well. Hence the greatest common factor is also called the Greatest Common Divisor (or) GCD. In the above example, the greatest common divisor (GCD) of 18 and 27 is 9 which can be written as:
GCD (18 , 27) = 9.
