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:
- Find all the factors of the smaller number.
- 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.