HCF of two or more numbers may be one of the numbers.
Step 1: Understand HCF.
The HCF (Highest Common Factor) is the biggest number that divides each of the given numbers exactly.
Step 2: When can HCF be one of the numbers?
If one number divides all the other numbers, that number itself can be the HCF.
Example 1:
Take 12 and 36.
Check division: \(12\mid 12\) and \(12\mid 36\).
So 12 is a common factor of both.
The common factors include \(1,2,3,4,6,12\).
The greatest among these is \(12\).
Therefore, \(\text{HCF}(12,36)=12\). Here, the HCF is one of the numbers.
Example 2:
Take 5 and 20.
Check division: \(5\mid 5\) and \(5\mid 20\).
So \(\text{HCF}(5,20)=5\). Again, the HCF equals one of the numbers.
Reason:
If a number \(a\) divides every other number, then \(a\) is a common factor of all.
No number bigger than \(a\) can divide \(a\) itself.
So \(a\) must be the highest common factor.
Conclusion:
The statement is true because the HCF can be one of the numbers when that number divides all the others.