Secondary 4 G2 Mathematics Tutor Bukit Timah | Prime Factorisation, HCF, LCM and Roots. Did you know? The numbers 36 and 48 share several factors, but their highest common factor is only 12. Their lowest common multiple is 144. Both answers become much easier to find when you break the numbers into primes rather than guessing from two long lists.
For a Secondary 4 G2 Mathematics learner in Bukit Timah, this is about more than divisibility. Prime factorisation is the common language of factors, multiples, perfect squares, perfect cubes and exact roots. Once the structure is visible, a student can reason through a question without repeatedly trying numbers on a calculator.
The official 2027 Singapore-Cambridge SEC G2 Mathematics K210 syllabus explicitly includes primes and prime factorisation, highest common factor (HCF), lowest common multiple (LCM), squares, cubes, square roots and cube roots by prime factorisation under N1: Numbers and their operations. A Secondary 4 student graduating in 2026 follows the applicable GCE N(A)-Level Mathematics Syllabus A 4045 instead. Check the 2026 syllabus directory and the 2027 G2 listing for the actual examination entry.
Quick answer: three number tools, three different questions
| What the question asks | Tool to use | What the answer must satisfy |
|---|---|---|
| How can the number be built from primes? | Prime factorisation | Multiply the prime powers to recover the original positive integer. |
| What is the biggest factor shared by two numbers? | HCF | It divides every stated number exactly. |
| What is the smallest positive multiple shared by two numbers? | LCM | It is divisible by every stated number. |
| What is a square root or cube root? | Group prime factors into pairs or triples | Raising the result to the corresponding power recovers the original number. |
The prime-factor method parents can teach in five steps
- Start with the smallest available prime: 2, then 3, 5, 7 and so on.
- Divide until only primes remain: avoid leaving a composite number labelled as prime.
- Write the product using powers: 72 = 2³ × 3².
- For HCF take common prime powers with the smallest exponents; for LCM take all present prime powers with the largest exponents.
- For square or cube roots: groups of two or three equal factors come outside the root, with the required check.
Did you know? The number 1 is not prime. A prime number has exactly two distinct positive divisors: 1 and itself. The number 1 has only one. Making this distinction prevents incorrect factor trees and prime-power answers.
Sixteen original worked examples from foundation to exam application
1. Factorise 84 into primes
84 = 2 × 42 = 2 × 2 × 21 = 2² × 3 × 7. Check: 4 × 3 × 7 = 84.
2. Factorise 126 into primes
126 = 2 × 63 = 2 × 3 × 21 = 2 × 3² × 7. All final bases—2, 3 and 7—are prime.
3. HCF of 84 and 126
Compare 84 = 2² × 3 × 7 and 126 = 2 × 3² × 7. Common smallest powers: 2 × 3 × 7 = 42.
4. LCM of 84 and 126
Keep the greatest powers from either number: 2² × 3² × 7 = 4 × 9 × 7 = 252.
5. HCF of 36 and 48
36 = 2² × 3²; 48 = 2⁴ × 3. Shared smallest powers give 2² × 3 = 12.
6. LCM of 36 and 48
The largest powers are 2⁴ × 3², so LCM = 16 × 9 = 144. Each input divides 144.
7. A second HCF pair
180 = 2² × 3² × 5 and 252 = 2² × 3² × 7. Shared prime powers give HCF = 36.
8. A second LCM pair
For 180 and 252, combine greatest prime powers: 2² × 3² × 5 × 7 = 1260.
9. A perfect square by prime powers
144 = 2⁴ × 3². Square-rooting halves the even exponents, giving √144 = 2² × 3 = 12.
10. Square root of 1296
1296 = 2⁴ × 3⁴. Group factors into pairs: √1296 = 2² × 3² = 36. Check 36² = 1296.
11. Cube root of 216
216 = 2³ × 3³. Each group of three contributes one factor, so ∛216 = 2 × 3 = 6.
12. Cube root of 1728
1728 = 2⁶ × 3³. Cube-rooting gives 2² × 3 = 12. Check 12³ = 1728.
13. Make 72 into a perfect square
72 = 2³ × 3². Its power of 2 is odd, so multiply by one more 2: 72 × 2 = 144 = 12². The smallest positive integer multiplier is 2.
14. Make 72 into a perfect cube
72 = 2³ × 3². The 2-exponent is already a multiple of three; one extra 3 makes 3³. Thus 72 × 3 = 216 = 6³ and the smallest multiplier is 3.
15. Sharing in identical groups
A teacher has 48 pencils and 72 pens. To make the maximum number of identical packs using every item, find HCF(48,72) = 24. Each of 24 packs has two pencils and three pens.
16. A recurring-event model
One event occurs every 12 days and another every 18 days, both starting together. The next joint recurrence is after LCM(12,18) = 36 days. This assumes perfectly regular intervals.
Why HCF and LCM answers must pass different tests
A good HCF result divides both numbers. A good LCM result is divisible by both numbers. They are not interchangeable: HCF often helps with grouping, sharing or maximum equal dimensions; LCM often helps with synchronising cycles or finding a common denominator.
For any two positive integers a and b, HCF(a,b) × LCM(a,b) = a × b. In the 36 and 48 example, 12 × 144 = 1728 and 36 × 48 = 1728. This identity is a useful independent arithmetic check; it does not replace the reasoning needed to select HCF or LCM for a word problem.
The first wrong step is a better diagnosis than ‘careless mistake’
| Student’s attempted step | Likely misunderstanding | A better correction |
|---|---|---|
| Writes 1 as prime | Definition of prime is uncertain | List all positive divisors of 1 and compare with 2, 3 and 5. |
| Stops a factor tree at 6 × 7 | Six is composite | Continue splitting until every leaf is prime. |
| Uses the largest exponents to find HCF | HCF/LCM rules reversed | Test whether the proposed HCF divides each input. |
| Uses only common factors to find LCM | Missing a necessary prime power | Check whether both inputs divide the result. |
| Turns √(2³ × 3²) into 2³ × 3 | Root does not act as identity | Group in pairs and check by squaring. |
| Calls any big number a perfect cube | Triple prime-power requirement not tested | Check whether each exponent is a multiple of three. |
Five changed questions to try before looking at answers
- Write 360 as a product of prime powers.
- Find HCF(72, 120).
- Find LCM(72, 120).
- Find √900 using prime factorisation.
- Find the smallest positive integer that multiplies 54 to make a perfect square.
Answers: (1) 2³ × 3² × 5; (2) 24; (3) 360; (4) 30 because 900 = 2² × 3² × 5²; (5) 6 because 54 = 2 × 3³ and 54 × 6 = 324 = 18². Check with multiplication rather than trusting an unlabelled calculator result.
A practical 90-minute three-pupil Mathematics tutorial
| Minutes | Learning activity | Independent evidence |
|---|---|---|
| 0–10 | Retrieval of prime definitions and simple factorizations | Student distinguishes a prime from a composite. |
| 10–25 | Three unseen HCF/LCM questions | Tutor identifies the first rule or factor-tree error. |
| 25–50 | Compare common-power and greatest-power decisions | Student explains why a factor or multiple is required. |
| 50–75 | Square roots, cube roots and short contextual models | Each learner selects a method without a topic prompt. |
| 75–90 | Exit question and planned delayed retest | Student solves a changed question alone days later. |
The unchanged eduKateSG Mathematics small-group tutorial reference describes premium three-pupil, 1.5-hour weekly tuition near Sixth Avenue MRT, with personal attention and guided correction. The example above illustrates a way to teach these number skills; it does not claim that a particular Secondary 4 G2 tutor, class, fee or vacancy is available.
A seven-day routine that actually checks understanding
- Day 1: prime-versus-composite number checks and ten factor trees.
- Day 2: calculate HCF using prime powers and division checks.
- Day 3: calculate LCM and verify shared multiples.
- Day 4: work on squares and square roots via paired prime factors.
- Day 5: work on cubes and cube roots via groups of three.
- Day 6: use unfamiliar word problems to decide HCF versus LCM.
- Day 7: retest two earlier errors with new numbers without notes.
Frequently asked questions
Are HCF and LCM still in the 2027 SEC G2 syllabus?
Yes. The 2027 K210 N1 content explicitly names highest common factor and lowest common multiple, alongside finding squares, cubes and roots through prime factorisation. Use the correct examination-year syllabus for the student’s actual cohort.
What is the fastest way to decide HCF or LCM?
Ask what the final quantity must do. The HCF is the largest divisor shared by the numbers; the LCM is the smallest positive number divisible by each. The meaning of the story determines the method, not the size of the original numbers.
Will a calculator replace factor trees?
A calculator can check numerical multiplication and roots, but a student may still need to present the prime-factor structure and justify why the chosen result is a highest common factor, lowest common multiple or exact root.
How can parents verify that tuition has helped?
Ask the student to choose the right technique from an unseen grouping or recurrence problem and explain the prime exponents after a delay. A correct answer copied while being shown is less convincing than an independent explanation.
Continue the Secondary 4 G2 Mathematics series
- Indices, standard form and number sense
- Ratios, percentages and financial Mathematics
- Equations and inequalities
- 2026 N(A) versus 2027 SEC revision
Official reading: SEAB 2026 N(A) syllabuses · SEAB 2027 SEC G2 syllabuses · SEAB 2027 K210 N1 syllabus. For enquiries about the published small-group teaching model, see the original eduKateSG tutorial page and eduKate Singapore. The worked questions are original educational examples, not SEAB examination items.