NCERT Solutions for Class 6th Maths Chapter 5 Prime Time
Updated on 2026-09-19
About this chapter
A multiple of a number is what you get on multiplying it by 1, 2, 3, … A factor (or divisor) of a number divides it exactly, leaving remainder 0. Numbers that are multiples of both numbers are their common multiples ; numbers that divide both are their common factors . A prime number has exactly two factors — 1 and itself (2, 3, 5, 7, 11, …). A composite number has more than two factors (4, 6, 8, 9, …). The number 1 is neither prime nor composite , as it has only one factor. The Sieve of Eratosthenes lists primes by circling a number and crossing out all its later multiples. It gives exactly 25 primes below 100 . Two numbers with no common factor other than 1 are co-prime — 4 and 9, 17 and 69, 40 and 231. Any two different primes are always co-prime. Every number greater than 1 can be writ
- Common Multiples and Common Factors
- Playing with other number pairs
- Jump Jackpot
- Prime Numbers
- Co-prime numbers for safekeeping treasures
- Prime Factorisation
- Using prime factorisation
- Divisibility Tests
- Fun with numbers
Quick revision
| Term | What it means | Example from the chapter | How to spot it |
|---|---|---|---|
| Multiple | The result of multiplying a number by 1, 2, 3, … | 3, 6, 9, 12, … are multiples of 3 | Is it in that number's table? |
| Factor (divisor) | A number that divides another exactly | 1, 2, 3, 4, 6, 8, 12, 24 are the factors of 24 | Does the division leave remainder 0? |
| Common multiple | A multiple of both numbers | 15, 30, 45, 60 for 3 and 5 | The 'idli-vada' numbers |
| Common factor | A factor of both numbers | 1 and 2 for 14 and 36 | Jump sizes that reach both treasures |
| Prime number | Has exactly two factors — 1 and itself | 2, 3, 5, 7, 11, 13, 17, 19 | Only one rectangular arrangement |
| Composite number | Has more than two factors | 4, 6, 8, 9, 10, 12, 14, 15 | More than one rectangle possible |
| The number 1 | Neither prime nor composite | 1 has only one factor | It stands alone |
| Sieve of Eratosthenes | Circle a number, cross out its later multiples | 25 primes lie below 100 | Whatever is left circled is prime |
| Twin primes | A pair of primes differing by 2 | 3 & 5, 11 & 13, 71 & 73 | Difference is exactly 2 |
| Co-prime numbers | No common factor other than 1 | 4 and 9; 40 and 231 | No common prime factor |
| Prime factorisation | A number written as a product of primes | 84 = 2 × 2 × 3 × 7 | Keep breaking till only primes are left |
| Perfect number | Sum of all its factors = twice the number | 6 and 28 | 1 + 2 + 3 + 6 = 12 = 2 × 6 |
Exercises
- In-text Question — Common Multiples and Common Factors Page 107
- Figure it Out — Common Multiples and Common Factors Page 108
- Playing with other number pairs — In-text Questions Page 108 & 109
- Jump Jackpot — In-text Questions Page 110
- Figure it Out — Common Multiples and Common Factors Page 110 & 111
- In-text Questions — Prime Numbers Page 112 to 114
- Figure it Out — Prime Numbers Page 114 & 115
- In-text Questions — Co-prime numbers for safekeeping treasures Page 115 to 117
- In-text Questions — Prime Factorisation Page 117 to 120
- Figure it Out — Prime Factorisation Page 120
- Using prime factorisation — Figure it Out Page 122
- In-text Questions — Divisibility Tests Page 123 to 125
- Figure it Out — Divisibility Tests Page 125 & 126
- In-text Questions — Fun with numbers Page 126 to 128