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. Check, from largest down, which of those divide the larger number exactly.

Once you find the biggest number that divides both, that’s your HCF.

Let’s walk through an example.

HCF of 12 and 18

Step-by-step:

  • Smaller number is 12.

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

  • Check from largest down:

    • $18 \div 12 = 1.5$ → ❌
    • $18 \div 6 = 3$ → ✅

So, the highest common factor is:

$$ \boxed{6} $$

How To Check Your Answer

You can reverse the process by checking the factors of the larger number.

  • Larger number is 18.

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

  • Filter out factors > 12: $[1, 2, 3, 6, 9]$

  • Check from largest down:

    • $12 \div 9 = 1.\overline{3}$ → ❌
    • $12 \div 6 = 2$ → ✅

Again, the HCF is:

$$ \boxed{6} $$

Summary

The highest common factor (HCF) of 12 and 18 is:

$$ \boxed{6} $$

This is the largest number that divides both 12 and 18 exactly.
This method is quick, reliable, and especially useful for reducing fractions.