Did you know? The number 1 is not prime, and 2 is the only even prime number. Those two facts help students make sense of primes, factors and multiples without having to memorise an endless list.
This guide is for families looking for a Secondary 3 G1 Mathematics tutor in Bukit Timah. G1 is a subject level under Singapore’s Full Subject-Based Banding. The SEAB directory for 2027 G1 syllabuses lists Mathematics as K110. The 2027 G1 Mathematics syllabus defines the whole-course content; schools may sequence Secondary 3 topics and school assessments differently. Prioritise the actual topics on your child’s school assessment schedule.
The quick answer: primes have exactly two positive factors
A prime number is a whole number greater than 1 with exactly two distinct positive factors: 1 and itself. A composite positive integer greater than 1 has more than two positive factors. The number 1 has only one positive factor, so it is neither prime nor composite.
The 2027 SEAB G1 K110 syllabus includes primes but explicitly excludes prime factorisation. That is an important distinction for parents: learning to recognise and reason about prime numbers is relevant, while prime factor trees should not be represented as an examinable K110 requirement.
Worked example 1: is 29 prime?
Question. Decide whether 29 is prime.
- Check the definition: 29 must have no positive factors other than 1 and 29.
- Try division by 2: 29 is odd, so 2 is not a factor.
- Try division by 3: the digits total 2 + 9 = 11, not a multiple of 3.
- Try division by 5: 29 does not end in 0 or 5.
- Conclude: 29 is prime. These checks suffice because any composite factor pair of 29 would include a factor no greater than √29, which is between 5 and 6.
The square-root observation is a useful checking explanation, not an instruction to start a more advanced factorisation topic. At this level, students should first understand how a number can be checked by ordinary divisibility and why one successful proper divisor proves a number is composite.
Worked example 2: why 21 is composite
Question. Is 21 a prime number?
- Test a possible divisor: 21 ÷ 3 = 7, with no remainder.
- List positive factors: 1, 3, 7, 21.
- Count: there are more than two different positive factors.
- Conclusion: 21 is composite, not prime.
A student does not need to find every factor to prove that 21 is not prime. Discovering the factor 3 is already enough. The full list is helpful for seeing the structure of the number, especially when comparing it with a truly prime number.
What is a factor? What is a multiple?
A factor divides a number exactly, leaving no remainder. A multiple is obtained by multiplying a number by a whole number. The two ideas work in opposite directions.
- Factors of 18: 1, 2, 3, 6, 9 and 18.
- Positive multiples of 18: 18, 36, 54, 72 and so on.
- Check a factor: 18 ÷ 6 = 3 exactly, so 6 is a factor of 18.
- Check a multiple: 18 × 4 = 72, so 72 is a multiple of 18.
The list of factors of a positive whole number is finite. Its positive multiples continue indefinitely. Ask your child to explain that difference in words. Knowing which direction the relationship goes prevents many errors when trying to find a number that divides evenly.
Worked example 3: packing an equal number of items
Imagine a fictional activity. A teacher has 24 identical tokens and wants to place them into equally sized packets with no leftovers. Is it possible to make packets of 4 tokens? Of 5 tokens?
- Packets of 4: 24 ÷ 4 = 6 exactly, so six packets work.
- Packets of 5: 24 ÷ 5 = 4 remainder 4, so equal packets of five leave tokens over.
- Interpret: 4 is a factor of 24; 5 is not.
- Check: 6 × 4 = 24 accounts for every token.
This is why divisibility matters in real contexts: students can connect factors to fair packing, repeated group sizes and shared arrangements. None of these examples requires decomposing a number into a formal prime-factor tree.
Why two is the only even prime
An even positive whole number greater than 2 is divisible by 2 and also by 1 and itself, so it has more than two positive factors. That makes it composite. The number 2 is the exception: its only positive factors are 1 and 2. Therefore it is prime.
This simple reasoning is more durable than the statement ‘even numbers are not prime’, which is incorrect because of 2. Good Mathematics teaching protects precise exceptions.
Common prime-number traps
Calling 1 the smallest prime
One is not prime because it does not have exactly two distinct positive factors. The smallest prime is 2.
Treating every odd number as prime
Nine is odd but 9 = 3 × 3, so it has a factor other than 1 and itself. Fifteen is also odd and divisible by 3 and 5. Oddness alone is not sufficient.
Assuming a large-looking number must be prime
Size is not the definition. For example, 91 looks unfamiliar but divides exactly by 7, giving 13, so it is composite. A quick divisibility check can settle the question.
Importing prime factorisation into the G1 examination scope
The official K110 N1 description names negative numbers and primes and says ‘exclude prime factorisation’. Students may encounter factors and multiples in foundational practice, but parents should not be told that lengthy prime-factor trees are required for this G1 examination.
A ten-minute number-sense routine
- List prime numbers from 2 to 20 by checking their positive factors.
- Explain why 1 is not on the list.
- Find the positive factors of 12 and 18.
- List the first four positive multiples of 6.
- Decide whether 29 is prime and whether 21 is composite, explaining why.
- Finish with the 24-token packing problem and one new group size.
Questions Bukit Timah parents often ask
Are prime numbers in the G1 syllabus?
Yes. The 2027 K110 syllabus includes primes, while specifically excluding prime factorisation.
Should my child memorise a long list of primes?
Recognising common small primes is useful, but understanding the two-factor definition and checking divisibility is more transferable than rote memorisation alone.
What should tuition focus on here?
The tutor should check divisibility, number relationships, exact arithmetic and explanations. Avoid confusing additional practice material with a compulsory examination requirement.
A useful next step for Bukit Timah parents
Choose one question from your child’s actual schoolwork and ask for a complete explanation of every step. A tutor can then locate the first uncertain decision rather than prescribe a large stack of generic worksheets. eduKateSG’s unchanged Secondary 1 Mathematics small-group reference describes guided corrections and close tutor attention near Sixth Avenue MRT. It is a reference for the teaching approach, not confirmation of a Secondary 3 G1 class timetable or vacancy. Enquire with eduKate Singapore about current suitable support.
Continue learning
- Percentages Above 100% and Growth
- Cones, Pyramids and Spheres
- 2027 SEC Paper 1 and Paper 2 Revision
- negative numbers and number lines
You can also check the exact national learning objectives in the SEAB K110 Mathematics syllabus.