Greatest Common Factor

What is GCF or What is Greatest Common Factor? 
GCF is the greatest of the common factors of the numbers.
By the definition of GCF, Greatest Common Factor is the largest number that factors into two or more greater numbers.
For instance, the GCF of 25 and 30 is 5, as 5 is the largest number that divides 25 and 30 evenly
Let us learn how to find GCF or how to find Greatest Common Factor:
First let us understand what factors are.
Factors are the numbers when multiplied together give another number

For instance, 4 x 6 = 24
4 and 6 are called the factors of 24
Now, let us understand what common factors are.
When we list out all the factors of given two or more numbers, the common factors are those found in both the lists.

For instance, factors of 18 and 24
18 = 1, 2, 3, 6, 9, 18
24 = 1, 2, 3, 4, 6, 8, 12, 24
The common factors from the above list are 1, 2, 3, and 6 as they appear in both the lists
To find the GCF of given two or more numbers, we follow a set of steps:
1. List out all the factors of the given numbers
2. From the list of factors, we need to list out all the factors that are common
3. The greatest of the common factors is the required GCF of the given numbers

Example: Find the GCF of 56,  84 and 112
Solution: Factors of,
56 = 1,2, 4,7, 8,14,28,56
       84= 1,2, 3,4,6,7, 12, 14,21,28,42,84
          112= 1,2,4,7, 8,14,16,28,56,112
Common factors from the above list are:
 1, 2, 4, 7, 14 and 28
Highest of the common factors is 28
So, the GCF of 56, 84 and 112 is 28

Greatest Common Divisor:
The Greatest Common Divisor or GCD of two numbers is in other words called Greatest common factor (GCF), which is the largest number that is a divisor (factor) of both the numbers.

Example of GCD

For instance, the largest number that divides both 24 and 18 is 6.