The HCF of two numbers is smaller than the smaller of the numbers.
Step 1: Recall the idea.
HCF means the greatest common factor of two numbers. Any common factor cannot be bigger than the smaller number, so the HCF is at most the smaller number.
In symbols (small steps):
\(\text{HCF}(a,b) \le \min(a,b)\)
Step 2: Check a counterexample.
Take both numbers equal: \(9\) and \(9\).
\(\text{HCF}(9,9) = 9\)
The smaller number is also \(9\).
Here, the HCF is equal to the smaller number, not smaller than it.
Step 3: Another simple case.
Take \(4\) and \(8\).
\(\text{HCF}(4,8) = 4\)
The smaller number is \(4\).
Again, the HCF equals the smaller number.
Conclusion.
The HCF can be equal to the smaller number (and not always strictly smaller).
Therefore, the statement “HCF is smaller than the smaller number” is false.