HCF is known as Highest Common Factor or Greatest Common Divisor (GCD) or Greatest Common Measure (GCM).
Factor: A number x is said to be factor of y when x exactly divides y.
Ex: Let’s say x = 3 and y = 15. Here 3(x) can exactly divide 15(y) so 3 is said to be factor of 15.
Lets take two numbers 80 and 30 for better understanding. Write factors of both numbers.
Factors of 30 : 1, 2, 3, 5, 6, 10, 15, 30
Factors of 80 : 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
There are many common factors for 80 and 30. Those are 1, 2, 5 and 10. But 10 is highest of them. So 10 is called Highest Common Factor or HCF of 80 and 30.
One thing is to be noted that HCF is less than or equal to the smallest number of the given numbers.
