Chapter 11 of 29

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CBSE Class 5 Mathematics★ 5-7 marks in Class 5 Mathematics assessments; multiples, factors, LCM, and HCF

Be My Multiple, I'll Be Your Factor

Be My Multiple, I'll Be Your Factor is a current Class 5 CBSE Mathematics chapter from NCERT Math Magic. These notes cover multiples, factors, prime and composite numbers, LCM, and HCF with number games and practice questions.

⏱ 12 min readEasy difficulty✓ Free · NCERT-aligned

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

1Find multiples and factors of numbers
2Distinguish prime and composite numbers
3Write a number as a product of prime factors
4Find the LCM of two numbers
5Find the HCF of two numbers

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Why this chapter matters

'Be My Multiple, I'll Be Your Factor' explores multiples, factors, prime and composite numbers, LCM, and HCF. These number-theory ideas underpin fractions, ratios, and algebra and appear in grouping, sharing, and divisibility problems.

Before you start — revise these

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

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Class 4 Mathematics: Multiplication tables

Times tables and division

Be My Multiple, I'll Be Your Factor — Class 5 Mathematics (CBSE)

Based on the NCERT Math Magic Grade 5 textbook. Understand multiples, factors, and number relationships, then solve the practice set without looking at the answers.

1. Why this chapter matters

Multiples and factors are building blocks of number theory. They help students understand the structure of numbers, find patterns, and solve problems involving grouping, sharing, and divisibility. This chapter introduces prime numbers, composite numbers, LCM (Lowest Common Multiple), and HCF (Highest Common Factor). These concepts are essential for fractions, ratios, and algebra in higher classes — and they also appear in puzzles, calendars, and everyday situations like arranging items in rows.

2. What are multiples?

A multiple of a number is the product of that number with any whole number (1, 2, 3, 4...).

Example: Multiples of 3 are: 3 x 1 = 3 3 x 2 = 6 3 x 3 = 9 3 x 4 = 12 3 x 5 = 15

So multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30...

Properties of multiples

Every number is a multiple of itself (e.g., 7 is a multiple of 7).
Every number is a multiple of 1.
Multiples of a number go on forever (infinite).
The smallest multiple of any number is the number itself.

Number	First 5 multiples
2	2, 4, 6, 8, 10
5	5, 10, 15, 20, 25
7	7, 14, 21, 28, 35
10	10, 20, 30, 40, 50
12	12, 24, 36, 48, 60

3. What are factors?

A factor of a number divides that number exactly (with no remainder).

Example: Factors of 12 are the numbers that divide 12 exactly: 12 / 1 = 12 (so 1 and 12 are factors) 12 / 2 = 6 (so 2 and 6 are factors) 12 / 3 = 4 (so 3 and 4 are factors) 12 / 4 = 3 (already listed) 12 / 6 = 2 (already listed)

Factors of 12 = 1, 2, 3, 4, 6, 12

Properties of factors

The smallest factor of any number is 1.
The largest factor of any number is the number itself.
Factors are finite (unlike multiples).
Every factor divides the number exactly (remainder = 0).

Prime factorisation

Breaking a number into its prime factors. For example: 12 = 2 x 2 x 3 = 2^2 x 3 20 = 2 x 2 x 5 = 2^2 x 5 36 = 2 x 2 x 3 x 3 = 2^2 x 3^2

4. Prime and composite numbers

Type	Definition	Example
Prime number	Has exactly 2 factors: 1 and itself	2, 3, 5, 7, 11, 13, 17, 19, 23
Composite number	Has more than 2 factors	4, 6, 8, 9, 10, 12, 14, 15, 16
1 (special)	Has only 1 factor (1 itself)	Neither prime nor composite

Prime numbers up to 50

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

How to check if a number is prime

Check if it is divisible by 2 (even numbers > 2 are not prime).
Check if it is divisible by 3 (sum of digits divisible by 3).
Check if it is divisible by 5 (ends in 0 or 5).
If none of these divide it exactly, it is likely prime.

5. Lowest Common Multiple (LCM)

The LCM of two or more numbers is the smallest number that is a multiple of all of them.

Method 1: Listing multiples

Find LCM of 4 and 6: Multiples of 4: 4, 8, 12, 16, 20, 24... Multiples of 6: 6, 12, 18, 24, 30... Common multiples: 12, 24... The smallest is 12. LCM(4, 6) = 12

Method 2: Prime factorisation

Find LCM of 8 and 12: 8 = 2 x 2 x 2 = 2^3 12 = 2 x 2 x 3 = 2^2 x 3 LCM = 2^3 x 3 = 8 x 3 = 24

6. Highest Common Factor (HCF)

The HCF (also called GCD) of two or more numbers is the largest number that divides all of them exactly.

Method 1: Listing factors

Find HCF of 12 and 18: Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 18: 1, 2, 3, 6, 9, 18 Common factors: 1, 2, 3, 6 The largest is 6. HCF(12, 18) = 6

Method 2: Prime factorisation

Find HCF of 24 and 36: 24 = 2 x 2 x 2 x 3 = 2^3 x 3 36 = 2 x 2 x 3 x 3 = 2^2 x 3^2 HCF = 2^2 x 3 = 4 x 3 = 12

7. Number games

Game 1 — Factor finder: Pick a number between 20 and 50. List all its factors. Your partner picks another number. Who has more factors?

Game 2 — Multiple maze: Start at 1. Move forward by adding any multiple of 2, 3, or 5. Reach exactly 50 in the fewest moves.

Game 3 — Sieve of Eratosthenes: Write numbers 1 to 100 on a grid. Cross out 1. Then cross out all multiples of 2 (except 2), then 3, then 5, then 7. The remaining numbers are prime.

8. Activity corner

Activity 1: Take 24 tokens (beads, buttons, stones). Arrange them in equal rows. How many different rectangular arrangements can you make? Each arrangement represents a factor pair of 24.

Activity 2: Find the LCM of (2, 3), (3, 4), (4, 5), (5, 6). What pattern do you notice?

Activity 3: Make a factor tree for 48, 60, and 72. Write each as a product of prime factors.

9. Common mistakes

Mistake: Confusing multiples and factors Fix: Remember — factors divide the number exactly; multiples are the number multiplied by other numbers.
Mistake: Thinking 1 is a prime number Fix: A prime has exactly two factors. 1 has only one factor (itself), so it is neither prime nor composite.
Mistake: Forgetting to check all divisors when finding factors Fix: Check systematically from 1 onwards. When you reach a number whose square is greater than the original, you have found all factors.

10. Key facts

Multiples = number x whole number (infinite).
Factors = numbers that divide exactly (finite).
Prime numbers have exactly 2 factors: 1 and itself.
Composite numbers have more than 2 factors.
1 is neither prime nor composite.
LCM is the smallest common multiple.
HCF is the largest common factor.
Every composite number can be expressed as a product of prime factors.

11. Self-test

List the first five multiples of 8.
Find all factors of 36.
Is 29 a prime number? Explain why or why not.
Find the LCM of 6 and 9.
Find the HCF of 16 and 24.

12. Answer key

List the first five multiples of 8. Answer: 8, 16, 24, 32, 40 (8 x 1, 8 x 2, 8 x 3, 8 x 4, 8 x 5).
Find all factors of 36. Answer: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Is 29 a prime number? Explain why or why not. Answer: Yes, 29 is prime. Its only factors are 1 and 29. It is not divisible by 2, 3, or 5.
Find the LCM of 6 and 9. Answer: Multiples of 6: 6, 12, 18, 24... Multiples of 9: 9, 18, 27... The LCM is 18.
Find the HCF of 16 and 24. Answer: Factors of 16: 1, 2, 4, 8, 16. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Common factors: 1, 2, 4, 8. HCF = 8.

13. Quick revision

Multiples are numbers you get by multiplying.
Factors are numbers that divide without remainder.
Prime = 2 factors only. Composite = more than 2.
LCM = smallest common multiple (useful for adding fractions).
HCF = largest common factor (useful for simplifying fractions).
Practise factor trees and listing multiples.
Play number games to build speed and confidence.

Key formulas & results

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

Prime vs composite

Prime has exactly 2 factors; composite has more than 2

1 is neither prime nor composite.

LCM and HCF

LCM = smallest common multiple; HCF = largest common factor

Found by listing or prime factorisation.

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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

✗ Confusing multiples and factors

✓ Factors divide the number exactly; multiples are the number multiplied by other whole numbers.

WATCH OUT

✗ Thinking 1 is a prime number

✓ A prime has exactly two factors; 1 has only one, so it is neither prime nor composite.

WATCH OUT

✗ Missing some factors

✓ List factors in pairs starting from 1; stop when the pairs begin to repeat.

NCERT exercises (with solutions)

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

Multiples and factors

Listing multiples, factors, primes, and composites

Questions

LCM and HCF

Finding LCM and HCF by listing and factorisation

Questions

Practice problems

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

Q1EASY· Multiples

List the first five multiples of 8.

▶ Show solution

8, 16, 24, 32, 40.

Q2EASY· Factors

Find all the factors of 36.

▶ Show solution

1, 2, 3, 4, 6, 9, 12, 18, 36.

Q3EASY· LCM

Find the LCM of 6 and 9.

▶ Show solution

18, the smallest number that is a multiple of both 6 and 9.

Q4EASY· HCF

Find the HCF of 16 and 24.

▶ Show solution

8, the largest factor common to both (factors 1, 2, 4, 8).

5-minute revision

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

•Multiples are a number times whole numbers (infinite).
•Factors divide a number exactly (finite).
•Prime numbers have exactly two factors; composites have more.
•1 is neither prime nor composite.
•Every composite can be written as a product of primes.
•LCM is the smallest common multiple.
•HCF is the largest common factor.

CBSE marks blueprint

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

Typical chapter weightage: 5-7 marks, depending on the school paper

Question type	Marks each	Typical count	What it tests
Multiples / factors	2-3	1-2	Listing multiples, factors, primes
LCM / HCF	3-4	1-2	Finding LCM and HCF

Prep strategy

Practise listing multiples and factors
Memorise primes up to 50
Learn LCM by listing common multiples
Find HCF using common factors or factor trees

Where this shows up in the real world

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

Arranging and grouping

Factors help arrange items in equal rows or groups.

Scheduling

LCM finds when repeating events happen together.

Simplifying fractions

HCF reduces fractions to their simplest form.

Exam strategy

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

List factors in pairs to avoid missing any
Use divisibility rules to spot factors
Find LCM as the smallest shared multiple
Find HCF as the largest shared factor

Going beyond the textbook

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

Use the Sieve of Eratosthenes to find primes up to 100.
Make factor trees for larger numbers like 72 and 90.

Where else this chapter is tested

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

CBSE Class 5 School ExamHigh

Maths Olympiad / IMOMedium

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Questions students ask

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

A factor of a number divides it exactly with no remainder, so the factors of 12 are 1, 2, 3, 4, 6, and 12. A multiple of a number is what you get when you multiply it by whole numbers, so the multiples of 12 are 12, 24, 36, 48, and so on. A number has only a limited set of factors but infinitely many multiples. A helpful way to remember: factors are smaller than or equal to the number, while multiples are greater than or equal to it.

The LCM and HCF make working with fractions much easier. When adding or subtracting fractions with different denominators, you use the LCM of the denominators as the common denominator. When simplifying a fraction to its lowest terms, you divide the numerator and denominator by their HCF. So learning to find the LCM and HCF directly helps you handle fractions correctly and quickly.

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