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Tamil Nadu (TNBSE)Class 6 Mathematics★ 8-12 marks in the TN Class 6 Term 2 exam through divisibility, prime factorisation, HCF and LCM sums

Numbers (Term 2) - Factors and Multiples

Samacheer Kalvi (TN State Board) Class 6 Maths — Term 2 Chapter 1, Numbers. Factors and multiples, the divisibility rules (2 to 11), prime and composite numbers and Eratosthenes' sieve, prime factorisation, and finding the HCF and LCM, with worked examples, exercises and quick revision.

⏱ 15 min readEasy difficulty✓ Free · NCERT-aligned

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By the end of this chapter you'll be able to…

1Find factors and multiples of a number
2Apply the divisibility rules
3Identify prime and composite numbers
4Write the prime factorisation of a number
5Find the HCF and LCM

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Why this chapter matters

Factors, multiples, HCF and LCM are core number-theory skills used in fractions, ratios and problem solving. They are high-weight, directly tested topics in the TN Class 6 Term 2 exam.

Before you start — revise these

A 5-minute refresher here will save you 30 minutes of confusion below.

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Term 1 — Numbers (Whole Numbers)

Multiplication and division.

Numbers (Factors and Multiples) — Class 6 Maths (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 6 Mathematics, Term 2 — Chapter 1. Factors, multiples, primes, HCF and LCM.

1. About this chapter

This chapter covers factors and multiples, the divisibility rules, prime and composite numbers (and the sieve of Eratosthenes), prime factorisation, and the HCF and LCM.

2. Factors, multiples and divisibility

A factor of a number divides it exactly (no remainder); a multiple is got by multiplying a number by 1, 2, 3 …
Divisibility rules:
- 2: last digit even (0, 2, 4, 6, 8). 5: ends in 0 or 5. 10: ends in 0.
- 3: digit sum divisible by 3. 9: digit sum divisible by 9.
- 4: last two digits divisible by 4. 6: divisible by 2 and 3. 11: difference of alternate digit sums is 0 or a multiple of 11.

3. Prime and composite numbers

A prime number has exactly two factors (1 and itself): 2, 3, 5, 7, 11 … 2 is the only even prime.
A composite number has more than two factors (4, 6, 8, 9 …). 1 is neither prime nor composite.
The sieve of Eratosthenes finds primes by crossing out multiples of each prime.

4. HCF and LCM

The HCF (Highest Common Factor) is the largest number that divides all the given numbers.
The LCM (Least Common Multiple) is the smallest number that is a multiple of all of them.
Both can be found by prime factorisation: HCF = product of common prime factors; LCM = product of all prime factors (highest powers).

5. Worked examples

Example 1. Is 348 divisible by 3? Digit sum 3 + 4 + 8 = 15, divisible by 3 → yes.

Example 2. Find the HCF of 12 and 18. 12 = 2² × 3, 18 = 2 × 3²; common = 2 × 3 = 6.

Example 3. Find the LCM of 4 and 6. 4 = 2², 6 = 2 × 3; LCM = 2² × 3 = 12.

6. Exercises (Samacheer Kalvi)

Write all the factors of 24.
Check the divisibility of 4,728 by 2, 3, 4 and 9.
List the prime numbers between 1 and 20.
Find the HCF of 16 and 24.
Find the LCM of 8 and 12.

7. Common mistakes

Mistake: Calling 1 a prime number. Fix: 1 is neither prime nor composite (it has only one factor).
Mistake: Mixing up HCF and LCM. Fix: HCF is the largest common factor; LCM is the smallest common multiple.
Mistake: Saying all even numbers are composite. Fix: 2 is even and prime.

8. Quick revision

Term 2 · Ch 1 · factors and multiples.
Factor divides exactly; multiple = number × 1, 2, 3 …
Divisibility: 2 (even), 3/9 (digit sum), 5 (0/5), 10 (0), 4 (last two), 6 (2 and 3), 11 (alternate sums).
Prime = 2 factors (2 only even prime); 1 is neither. HCF = largest common factor; LCM = smallest common multiple (via prime factorisation).

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Divisibility

2 (even), 3/9 (digit sum), 5 (0/5), 4 (last two), 11 (alternate sums)

Quick tests.

Prime / composite

prime = 2 factors; composite = more than 2

1 is neither; 2 is the only even prime.

HCF

product of common prime factors

Largest common factor.

LCM

product of all prime factors (highest powers)

Smallest common multiple.

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Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Calling 1 a prime number

✓ 1 is neither prime nor composite (it has only one factor).

WATCH OUT

✗ Mixing up HCF and LCM

✓ HCF is the largest common factor; LCM is the smallest common multiple.

WATCH OUT

✗ Saying all even numbers are composite

✓ 2 is even and prime.

NCERT exercises (with solutions)

Every NCERT exercise from this chapter — what it covers and how many questions to expect.

Factors and divisibility

List factors and test divisibility.

Questions

Primes

Identify primes; use the sieve.

Questions

HCF and LCM

Find HCF and LCM by prime factorisation.

Questions

Practice problems

Try each one yourself before tapping "Show solution". Active recall > rereading.

Q1EASY· Factors

Write all the factors of 24.

▶ Show solution

1, 2, 3, 4, 6, 8, 12, 24.

Q2EASY· Divisibility

Is 348 divisible by 3?

▶ Show solution

Digit sum 15 is divisible by 3, so yes.

Q3EASY· Primes

List the prime numbers between 1 and 20.

▶ Show solution

2, 3, 5, 7, 11, 13, 17, 19.

Q4MEDIUM· HCF

Find the HCF of 16 and 24.

▶ Show solution

16 = 2⁴, 24 = 2³ × 3; HCF = 2³ = 8.

Q5MEDIUM· LCM

Find the LCM of 8 and 12.

▶ Show solution

8 = 2³, 12 = 2² × 3; LCM = 2³ × 3 = 24.

Q6MEDIUM· Divisibility

Check 4,728 for divisibility by 4 and 9.

▶ Show solution

Last two digits 28 ÷ 4 = 7 → divisible by 4; digit sum 21 not divisible by 9 → not by 9.

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•Term 2 Chapter 1 of Samacheer Kalvi Class 6 Maths.
•A factor divides exactly; a multiple is the number times 1, 2, 3 …
•Divisibility rules: 2 (even), 3/9 (digit sum), 5 (0/5), 4 (last two), 6 (2 and 3), 11 (alternate sums).
•Prime = exactly two factors; 2 is the only even prime; 1 is neither.
•HCF = product of common prime factors (largest common factor).
•LCM = product of all prime factors at highest powers (smallest common multiple).

Tamil Nadu (TNBSE) marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Typical chapter weightage: 8-12 marks across number theory

Question type	Marks each	Typical count	What it tests
Objective	1	3-4	Factors, divisibility, primes
HCF	2	1-2	Highest common factor
LCM	2	1-2	Least common multiple

Prep strategy

Memorise the divisibility rules
Practise prime factorisation
HCF = common factors; LCM = all factors
Remember 1 is neither prime nor composite

Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

Fractions

HCF simplifies fractions; LCM finds common denominators.

Scheduling

LCM finds when repeating events coincide.

Grouping

HCF splits items into equal largest groups.

Exam strategy

Battle-tested tips from teachers and toppers for this chapter.

Apply the divisibility rule before dividing
Show the prime factorisation
Pick common factors for HCF, all for LCM
State the rule used

Going beyond the textbook

For olympiad aspirants and curious learners — topics that build on this chapter.

Find the smallest number divisible by 6, 8 and 12.
Two bells ring every 15 and 20 minutes. When do they ring together?

Where else this chapter is tested

CBSE board isn't the only one — other exams test this chapter too.

TN Class 6 Term 2 ExamHigh

NMMS / Foundation MathsHigh

School unit testsHigh

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Questions students ask

The real ones — pulled from the Q&A community and tutor sessions.

The HCF is the largest number that divides all the given numbers, while the LCM is the smallest number that is a multiple of all of them.

A prime number must have exactly two different factors — 1 and itself — but 1 has only a single factor, so it is neither prime nor composite.

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