Some students lose marks in Mathematics not because the topic is hard, but because they skip the quiet small steps that hold the whole answer together.
HCF is one of those topics.
On paper, it looks simple.
Find the factors.
Circle the common ones.
Take the biggest one.
Done.
But once the child starts rushing, trouble begins.
They forget factors.
They miss a number.
They confuse factors with multiples.
They stop too early.
And just like that, a 1-mark or 2-mark question becomes a silly leak in the exam.
That is why I actually like teaching HCF slowly.
Because when a student learns to do this carefully, something good happens. They start respecting structure. They stop guessing. They realise that Math is not just about getting to the answer. It is about walking the correct path to the answer.
And for many children, that is a very important upgrade.
So let us do this properly.
Not in a rushed classroom blur.
Not in a panicky worksheet scramble.
But step by step.
What is HCF again?
HCF means Highest Common Factor.
That means:
- factor = a number that divides exactly into another number
- common = shared by both numbers
- highest = the biggest one
So if we want the HCF of two numbers, we are asking:
What is the biggest number that can divide both numbers exactly?
That is all.
Before anything fancy, that meaning must be stable first.
Because if a child does not understand that sentence properly, the working becomes blind.
What does “listing factors” mean?
Listing factors means writing down all the numbers that divide exactly into a given number.
For example:
Factors of 12 are:
1, 2, 3, 4, 6, 12
Why?
Because all these numbers divide into 12 with no remainder.
That is what we mean by factors.
So when we use the listing factors method for HCF, we do three things:
- List all factors of the first number
- List all factors of the second number
- Find the common factors and choose the highest one
That is the whole method.
Simple, yes.
But only if the student is careful.
Step 1: List the factors of the first number
Let us find the HCF of 18 and 24.
Start with 18.
Ask:
Which numbers divide exactly into 18?
The factors of 18 are:
1, 2, 3, 6, 9, 18
That is the full list.
Now, many students make the mistake of writing only some of them.
Maybe they forget 1.
Maybe they forget 6.
Maybe they stop at 3.
Maybe they rush.
That is why neatness matters.
Do not just scribble random numbers and hope the truth appears.
List them clearly.
Step 2: List the factors of the second number
Now do the same for 24.
Which numbers divide exactly into 24?
The factors of 24 are:
1, 2, 3, 4, 6, 8, 12, 24
Again, write them carefully.
At this stage, there is no need to panic. No need to be clever. No need to rush.
Just be accurate.
Math rewards accurate children more than dramatic children.
Step 3: Find the common factors
Now compare the two lists.
Factors of 18:
1, 2, 3, 6, 9, 18
Factors of 24:
1, 2, 3, 4, 6, 8, 12, 24
Which numbers appear in both lists?
The common factors are:
1, 2, 3, 6
These are the numbers shared by both 18 and 24.
Step 4: Choose the highest one
Now take the biggest of the common factors.
The common factors are:
1, 2, 3, 6
The highest is:
6
So the HCF of 18 and 24 is 6.
That is the complete method.
Nothing magical.
Just careful thinking.
A second example
Let us find the HCF of 20 and 30.
Factors of 20
1, 2, 4, 5, 10, 20
Factors of 30
1, 2, 3, 5, 6, 10, 15, 30
Common factors
1, 2, 5, 10
Highest common factor
10
So the HCF of 20 and 30 is 10.
Again, clean and simple.
A third example
Now let us do 12 and 16.
Factors of 12
1, 2, 3, 4, 6, 12
Factors of 16
1, 2, 4, 8, 16
Common factors
1, 2, 4
Highest common factor
4
So the HCF of 12 and 16 is 4.
This is the kind of question children should be able to do comfortably before moving into word problems.
How to list factors without missing numbers
This is where students often get careless.
They know the idea, but they miss one factor and the answer collapses.
A good habit is this:
Start from 1 and work upward.
Ask:
- Does 1 divide exactly?
- Does 2 divide exactly?
- Does 3 divide exactly?
- Does 4 divide exactly?
And so on.
This is not glamorous, but it works.
For example, for 18:
- 1 yes
- 2 yes
- 3 yes
- 4 no
- 5 no
- 6 yes
- 7 no
- 8 no
- 9 yes
- 10 and above need not continue once the pairings become obvious
Over time, students get faster at recognising factors.
But in the beginning, slow and careful is better than fast and wrong.
A faster trick: factor pairs
This is a useful shortcut.
Instead of testing every number one by one, look for factor pairs.
For example, for 24:
1 × 24
2 × 12
3 × 8
4 × 6
So the factors are:
1, 2, 3, 4, 6, 8, 12, 24
This is a neat method because it helps students organise their thinking.
For 18:
1 × 18
2 × 9
3 × 6
So the factors are:
1, 2, 3, 6, 9, 18
Very clean.
This method reduces missing numbers.
And anything that reduces silly mistakes is worth teaching.
The most common mistakes students make
1. Forgetting 1
Every whole number has 1 as a factor.
Always.
It may look unimportant, but forgetting 1 shows the child is not thinking in a stable way yet.
2. Confusing factors with multiples
This is a big one.
Factors divide into the number.
Multiples are what you get when you multiply.
If a student writes:
Factors of 12 = 12, 24, 36…
that is not factors. That is multiples.
This confusion must be corrected early.
3. Missing a factor in the middle
A child may write:
Factors of 24 = 1, 2, 3, 4, 8, 12, 24
and forget 6.
That one missing number may ruin the answer.
4. Choosing a common factor, but not the highest one
For example, the child sees that 2 is common and writes 2 as the answer, forgetting that 6 is also common.
That is not enough.
HCF means the highest common factor.
Not just any common factor.
5. Rushing because the question looks easy
This topic is dangerous precisely because it looks harmless.
Children relax too much.
Then they miss something small.
Then the marks go.
That is why steady thinking matters.
A simple check after finding the answer
Once a student gets the HCF, they should ask:
Does this number divide both original numbers exactly?
For example, if the student says the HCF of 18 and 24 is 6:
- 18 ÷ 6 = 3
- 24 ÷ 6 = 4
Yes, both divide exactly.
Good.
Now ask:
Is there any bigger common factor?
No.
So 6 is correct.
This checking habit is very important. It helps students catch careless mistakes before the exam paper goes in.
When is the listing factors method good?
This method is best when:
- the numbers are not too large
- the child is still learning the concept
- the goal is understanding, not speed
- the teacher wants to build a strong foundation first
For smaller numbers, listing factors is excellent because it shows the meaning clearly.
The child can actually see the common factors.
That visibility matters.
Later on, students may use prime factorisation for larger numbers.
But first, they should understand what HCF really is.
Otherwise, prime factorisation becomes just another procedure with no soul.
Why this method is good for weak students
Because it is concrete.
Some children get overwhelmed by abstract rules and fancy-looking steps.
But listing factors is direct.
You can see it.
You can compare it.
You can circle it.
You can explain it.
That makes it a very good teaching method for children who need the fog cleared.
Not every child needs speed first.
Some need clarity first.
And once clarity is built, speed comes much more naturally.
A worked example in full exam style
Let us write it neatly the way a student might show it in school.
Find the HCF of 18 and 24.
Factors of 18 = 1, 2, 3, 6, 9, 18
Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
Common factors = 1, 2, 3, 6
HCF = 6
That is enough.
Neat. Simple. Easy to follow.
Some students think more working means more intelligence.
Not true.
Clear working is better than messy heroics.
Practice questions for students
Try these using the listing factors method:
- Find the HCF of 8 and 12
- Find the HCF of 15 and 25
- Find the HCF of 14 and 21
- Find the HCF of 16 and 20
- Find the HCF of 27 and 36
These are good training questions because they are manageable, but still force the child to be careful.
Answers
- HCF of 8 and 12 = 4
- HCF of 15 and 25 = 5
- HCF of 14 and 21 = 7
- HCF of 16 and 20 = 4
- HCF of 27 and 36 = 9
Parents do not need to overcomplicate home practice.
A few clean questions done properly is often better than twenty rushed ones.
How parents can help at home
If your child is doing this topic, do not immediately ask:
“What is the answer?”
Instead ask:
- What are the factors of the first number?
- What are the factors of the second number?
- Which ones are common?
- Which is the highest?
That sequence teaches thinking.
And that matters far more than just blurting out the correct final number.
Because a child who understands the route can repeat success.
A child who only copies answers cannot.
What I watch for at Bukit Timah Tutor
When a student struggles with HCF by listing factors, I am usually checking:
- does the child know what a factor is?
- does the child miss numbers while listing?
- does the child understand what “common” means?
- does the child remember to choose the highest one?
- does the child rush because the topic looks easy?
These small things tell me whether the issue is concept, carelessness, or confidence.
Very often, once these are cleaned up, the child improves quickly.
Because many students are not bad at Math.
They are simply messy in method.
That is fixable.
The deeper lesson in this topic
HCF by listing factors teaches a child something very useful:
slow down, list clearly, compare properly, then decide
That pattern is bigger than this chapter.
It is good thinking.
Too many children want to jump straight to the final answer because they think speed looks smart.
But in school, and later in life, many problems are solved not by wild speed, but by patient structure.
That is what this little topic quietly teaches.
And that is why I like it.
Final thoughts
Finding HCF by listing factors is not difficult.
But it does require care.
That is the part many students underestimate.
The good news is that once the child understands the method clearly, HCF becomes one of those topics that can actually build confidence.
Because it is logical.
It is visual.
It is steady.
And when done properly, it works beautifully.
So if your child keeps slipping here, do not panic.
Go back to the basics.
List the factors.
Find the common ones.
Choose the highest one.
Sometimes improvement in Math is not about learning something new.
Sometimes it is about finally doing the simple thing properly.
Quick recap
To find HCF by listing factors:
Step 1
List all the factors of the first number
Step 2
List all the factors of the second number
Step 3
Find the common factors
Step 4
Choose the highest common factor
Example:
Factors of 18 = 1, 2, 3, 6, 9, 18
Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
Common factors = 1, 2, 3, 6
HCF = 6
Simple. Clean. Reliable.
