What’s the fastest way to find the highest common factor (HCF) of two numbers — and how can you check your answer?

The quickest method is:

  1. Find all the factors of the smaller number.
  2. From the largest factor down, test whether it also divides the larger number exactly.

Once you find such a factor, stop. That’s your HCF.

HCF of 32 and 48

Step-by-step process:

  • Smaller number is 32

  • Factors of 32: $[1, 2, 4, 8, 16, 32]$

  • Check which divide 48:

    • $48 \div 32 = 1.5$ → ❌
    • $48 \div 16 = 3$ → ✅

So the HCF is:

$$ \boxed{16} $$

How To Check Your Answer

Now reverse it and check from the larger number.

  • Larger number is 48

  • Factors of 48: $[1, 2, 3, 4, 6, 8, 12, 16, 24, 48]$

  • Remove factors greater than 32 → $[1, 2, 3, 4, 6, 8, 12, 16, 24]$

  • Check which divide 32:

    • $32 \div 24 = 1.33$ → ❌
    • $32 \div 16 = 2$ → ✅

Again, the HCF is 16.

Summary

The highest common factor (HCF) of 32 and 48 is:

$$ \boxed{16} $$

It’s the largest number that divides both 32 and 48 exactly.
This technique is especially helpful for reducing fractions and solving arithmetic problems efficiently.