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 26 and 36.

HCF of 26 and 36

Step-by-step:

  • Smaller number is 26

  • Factors of 26: $[1, 2, 13, 26]$

  • Check from largest down:

    • $36 \div 26 = 1.38$ → ❌
    • $36 \div 13 = 2.77$ → ❌
    • $36 \div 2 = 18$ → ✅

So the highest common factor is:

$$ \boxed{2} $$

How To Check Your Answer

Now check the factors of the larger number.

  • Larger number is 36

  • Factors of 36: $[1, 2, 3, 4, 6, 9, 12, 18, 36]$

  • Remove factors greater than 26 → $[1, 2, 3, 4, 6, 9, 12, 18]$

  • Check from largest down:

    • $26 \div 18 = 1.44$ → ❌
    • $26 \div 12 = 2.17$ → ❌
    • $26 \div 9 = 2.89$ → ❌
    • $26 \div 6 = 4.33$ → ❌
    • $26 \div 4 = 6.5$ → ❌
    • $26 \div 3 = 8.67$ → ❌
    • $26 \div 2 = 13$ → ✅

Same result — the HCF is 2.

Summary

The highest common factor (HCF) of 26 and 36 is:

$$ \boxed{2} $$

This is the largest number that divides both 26 and 36 exactly.
Knowing how to find the HCF is especially useful for simplifying fractions and solving other arithmetic problems.