Greatest Common Divisor - GCD
The Greatest Common Divisor (GCD) refers to the greatest number that is a
common divisor for a given set of numbers. It is also termed as the Highest
Common Factor (HCF) or the Greatest Common Factor (GCF). In this lesson, we
will learn how to find the greatest common divisor in detail.
What is Greatest Common Divisor?
For a set of positive integers (a, b), the greatest common divisor is defined as the
greatest positive!number!which is a common factor of both the positive!integers!(a,
b). GCD of any two numbers is never negative or 0 as the least positive integer
common to any two numbers is always 1.
GCD Meaning - GCD Full Form
The meaning and full form of GCD is the Greatest Common Divisor. So, GCD is
the greatest positive number which is a common divisor for a given set of positive
numbers.
How to Find the Greatest Common Divisor?
For a set of two positive integers (a, b) we use the following steps to find the
greatest common divisor:
GCD of Two Numbers
Let us see the steps given below to learn how to find the GCD of two numbers.
Step 1:!Write the divisors of the number 'a'.
Step 2:!Write the divisors of the number 'b'.
Step 3:!List the common divisors of 'a' and 'b'.
Step 4:!Now find the divisor which is the highest among the common divisors.
Example:!Find the greatest common divisor of 13 and 48.
Solution:!We will use the following steps to find the greatest common divisor of
(13, 48).
Divisors of 13 = 1, and 13.
Divisors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
The common divisor of 13 and 48 is 1.
The greatest common divisor of 13 and 48 is 1.
