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 to:

  1. Find all the factors of the smaller number.
  2. Check, starting from the largest, which one divides the larger number exactly.

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

Let’s look at an example.

HCF of 8 and 12

Step-by-step:

  • The smaller number is 8.

  • Factors of 8: $[1, 2, 4, 8]$

  • Check from largest down:

    • $12 \div 8 = 1.5$ → ❌
    • $12 \div 4 = 3$ → ✅

So, the highest common factor is:

$$ \boxed{4} $$

How To Check Your Answer

You can reverse the process by finding the factors of the larger number, and checking which divide into the smaller number.

  • Larger number is 12.

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

  • Filter those ≤ 8: $[1, 2, 3, 4, 6]$

  • Check:

    • $8 \div 6 = 1.33$ → ❌
    • $8 \div 4 = 2$ → ✅

Again, the HCF is:

$$ \boxed{4} $$

Summary

The highest common factor (HCF) of 8 and 12 is:

$$ \boxed{4} $$

This is the largest number that can divide both 8 and 12 exactly.

Knowing how to find the HCF is especially helpful when simplifying fractions and solving other arithmetic problems.