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

The most efficient method is:

  1. Find all the factors of the smaller number.
  2. Starting from the largest factor, check which ones also divide the larger number exactly.

As soon as one does — that’s your HCF.

Let’s try this with 32 and 24.

HCF of 32 and 24

Step-by-step:

  • Smaller number is 24

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

  • Check from largest down:

    • $32 \div 24 = 1.33$ → ❌
    • $32 \div 12 = 2.66$ → ❌
    • $32 \div 8 = 4$ → ✅

So the highest common factor is:

$$ \boxed{8} $$

How To Check Your Answer

Now check the factors of the larger number.

  • Larger number is 32

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

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

  • Check from largest down:

    • $24 \div 16 = 1.5$ → ❌
    • $24 \div 8 = 3$ → ✅

Again, the HCF is 8.

Summary

The highest common factor (HCF) of 32 and 24 is:

$$ \boxed{8} $$

This is the largest number that divides both 32 and 24 exactly.
Knowing how to find the HCF is especially useful when simplifying fractions and solving arithmetic problems.