NCERT Class 6 Maths Chapter 5 Prime Time | Complete Explanation + Solutions | Ganita Prakash

NCERT Class 6 Maths Chapter 5

Prime Time – Complete Explanation & Solutions

Introduction

Numbers appear everywhere in mathematics, but some numbers have special properties that make them very important. In this chapter, we explore the world of factors, multiples, prime numbers, and divisibility rules.

This chapter also introduces interesting mathematical games such as the Idli-Vada Game and Treasure Jump Game, which help us understand how numbers behave.

By the end of this chapter, students will learn:

• Multiples and common multiples

• Factors and common factors

• Prime and composite numbers

• Co-prime numbers

• Prime factorisation

• Divisibility tests

These ideas form the foundation for many topics in higher mathematics.

5.1 Common Multiples and Common Factors

Idli-Vada Game

Children count numbers in order:

• Say Idli for multiples of 3

• Say Vada for multiples of 5

• Say Idli-Vada for multiples of both

Example:

Multiples of 3
3, 6, 9, 12, 15, 18, 21 …

Multiples of 5
5, 10, 15, 20, 25 …

Common multiples of 3 and 5

15, 30, 45, 60 …

Important Concept

A number that is a multiple of both numbers is called a Common Multiple.

Example

Common multiples of 3 and 5

15, 30, 45, 60 …

Key Definitions

Factor

If a number divides another number exactly, it is called a factor.

Example
4 is a factor of 12 because

12 ÷ 4 = 3

Multiple

A multiple of a number is obtained by multiplying that number by integers.

Example

Multiples of 4

4, 8, 12, 16, 20 …

Common Factors

Factors that are common between two numbers.

Example

Factors of 20
1,2,4,5,10,20

Factors of 28
1,2,4,7,14,28

Common factors

1,2,4

Section 5.1 – Figure It Out Solutions

Question 1

At what number is Idli-Vada said for the 10th time?

Multiples of both 3 and 5 = multiples of 15

15 × 10 = 150

Answer

150

Question 2

Game played till 90

(a) Times children say Idli

Multiples of 3 up to 90

90 ÷ 3 = 30

Answer

30 times

(b) Times children say Vada

Multiples of 5 up to 90

90 ÷ 5 = 18

Answer

18 times

(c) Times children say Idli-Vada

Multiples of 15

90 ÷ 15 = 6

Answer

6 times

Question 3

Game till 900

Multiples of 3 = 900 ÷ 3 = 300
Multiples of 5 = 900 ÷ 5 = 180
Multiples of 15 = 900 ÷ 15 = 60

Answer

Idli = 300
Vada = 180
Idli-Vada = 60

5.2 Prime Numbers

Some numbers can only be divided by 1 and themselves.

These are called Prime Numbers.

Examples

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

Composite Numbers

Numbers having more than two factors.

Examples

4, 6, 8, 9, 10, 12

Important Fact

1 is neither prime nor composite.

Finding Prime Numbers

Sieve of Eratosthenes Method

Steps

1. Write numbers 1–100

2. Cross out 1

3. Circle 2 and remove multiples

4. Circle 3 and remove multiples

5. Continue the process

Remaining numbers are prime numbers.

Section 5.2 Questions

Q: Which numbers are prime?

23, 51, 37, 26

Check divisibility

23 → Prime
51 → divisible by 3
37 → Prime
26 → divisible by 2

Answer

Prime numbers

23, 37

Twin Prime Numbers

Two primes whose difference is 2

Examples

3 and 5
11 and 13
17 and 19

5.3 Co-Prime Numbers

Two numbers are co-prime if they have only one common factor → 1.

Example

4 and 9

Factors of 4
1,2,4

Factors of 9
1,3,9

Common factor = 1

Therefore

4 and 9 are co-prime.

5.4 Prime Factorisation

Prime factorisation means expressing a number as a product of prime numbers.

Example

56

56 = 2 × 2 × 2 × 7

Prime factors

2 and 7

Example

Find prime factorisation of 72

72 = 12 × 6
12 = 2 × 2 × 3
6 = 2 × 3

Therefore

72 = 2 × 2 × 2 × 3 × 3

Section 5.4 – Exercise Solutions

Question

Find prime factorisation of 64

64 ÷ 2 = 32
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1

Answer

64 = 2⁶

Question

Prime factorisation of 105

105 ÷ 3 = 35
35 ÷ 5 = 7

Answer

105 = 3 × 5 × 7

5.5 Divisibility Rules

These rules help check divisibility quickly.

Divisible by 2

Last digit must be

0,2,4,6,8

Example

682 → divisible by 2

Divisible by 5

Last digit must be

0 or 5

Example

125 → divisible by 5

Divisible by 10

Last digit must be

0

Example

8560 → divisible by 10

Divisible by 4

Last two digits must be divisible by 4.

Example

8536

36 ÷ 4 = 9

Therefore divisible by 4.

Divisible by 8

Last three digits must be divisible by 8.

Example

8560

560 ÷ 8 = 70

Therefore divisible by 8.

Summary of the Chapter

Important ideas from this chapter:

• Prime numbers have exactly two factors
• Composite numbers have more than two factors
• Prime factorisation expresses numbers as product of primes
• Co-prime numbers share only one common factor
• Divisibility rules simplify calculations

These concepts help in understanding LCM, HCF, algebra and number theory in later classes

 

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