Summary
Chapter 5 of the Class 6 Maths NCERT textbook (Ganita Prakash), "Prime Time", teaches prime and composite numbers, prime factorisation, co-prime numbers, and divisibility tests for 2, 4, 5, 8, and 10 through activities like the Idli-Vada game and Jump Jackpot treasure hunt.
- Prime and composite numbers — Primes have exactly two factors (1 and themselves) while composites have more, and 1 is neither. The Sieve of Eratosthenes finds every prime by systematically crossing out the multiples of each number.
- Prime factorisation and co-primes — Every number above 1 breaks into a unique set of prime factors, the building blocks of that number. Two numbers are co-prime when their only shared factor is 1, such as 4 and 9.
- Quick divisibility tests — Simple last-digit rules decide divisibility without dividing: check the final digit for 2, 5 and 10, the last two digits for 4, and the last three digits for 8, making mental checks fast.
Key points & formulas
- 01Prime numbers have exactly two factors — 1 and the number itself. First few primes: 2, 3, 5, 7, 11, 13, 17, 19.
- 02Composite numbers have more than two factors. First few composites: 4, 6, 8, 9, 10, 12.
- 03The number 1 is neither prime nor composite — it has only one factor.
- 042 is the only even prime number; all other even numbers are composite.
- 05The Sieve of Eratosthenes finds all primes by crossing out 1, then circling each uncircled number and crossing out all its multiples.
- 06Every number greater than 1 has a unique prime factorisation (the prime factors can be in any order, but the set of prime factors is unique).
- 07Two numbers are co-prime if their only common factor is 1. Example: 4 and 9 are co-prime; 15 and 39 are not (both share factor 3).
- 08Divisibility by 2: last digit is 0, 2, 4, 6, or 8. Divisibility by 5: last digit is 0 or 5. Divisibility by 10: last digit is 0.
- 09Divisibility by 4: the number formed by the last two digits must be divisible by 4. Divisibility by 8: the number formed by the last three digits must be divisible by 8.
- 10A perfect number is one where the sum of all its factors equals twice the number. 6 (factors: 1+2+3+6=12=2×6) and 28 are perfect numbers.
Frequently asked questions
01What is Chapter 5 Prime Time about in Class 6 Maths?
Chapter 5 Prime Time from Ganita Prakash Class 6 covers prime numbers, composite numbers, the Sieve of Eratosthenes, prime factorisation, co-prime numbers, and divisibility tests for 2, 4, 5, 8, and 10.
02What is the difference between prime and composite numbers?
Prime numbers have exactly two factors — 1 and themselves (e.g., 2, 3, 5, 7). Composite numbers have more than two factors (e.g., 4, 6, 9). The number 1 is special — it is neither prime nor composite.
03What is prime factorisation and why is it unique?
Prime factorisation means writing a number as a product of prime numbers. For example, 56 = 2 × 2 × 2 × 7. Every number greater than 1 has exactly one prime factorisation — the same prime factors appear no matter how you break the number down, only the order may vary.
04What are co-prime numbers? Give an example.
Two numbers are co-prime if their only common factor is 1. Example: 4 and 9 are co-prime because factors of 4 are 1,2,4 and factors of 9 are 1,3,9 — they share only 1. But 15 and 39 are not co-prime because both have 3 as a common factor.
05How do you check if a number is divisible by 4?
Look at the last two digits of the number. If the number formed by those two digits is divisible by 4, then the whole number is divisible by 4. For example, 8536 — last two digits are 36, and 36 ÷ 4 = 9, so 8536 is divisible by 4.
06How do you check if a number is divisible by 8?
Look at the last three digits of the number. If the three-digit number they form is divisible by 8, then the original number is divisible by 8. For example, 8576 — last three digits are 576, and 576 ÷ 8 = 72, so 8576 is divisible by 8.
07What is the Sieve of Eratosthenes and how does it work?
The Sieve of Eratosthenes is a method to find all prime numbers developed by Greek mathematician Eratosthenes about 2200 years ago. You cross out 1, then circle the smallest uncircled number and cross out all its multiples. Repeating this leaves only prime numbers circled.
08What are twin primes? Give examples from the chapter.
Twin primes are pairs of prime numbers with a difference of 2. Examples from the chapter include (3,5), (5,7), (11,13), (17,19), (29,31), (41,43), (59,61), and (71,73).
09What is the Idli-Vada game and what concept does it teach?
In the Idli-Vada game, children say 'idli' for multiples of one number, 'vada' for another, and 'idli-vada' for common multiples. The game teaches common multiples and the least common multiple (LCM). For multiples of 3 and 5, 'idli-vada' is first said at 15 — the smallest common multiple.
10How is prime factorisation used to check if one number divides another?
A number A is divisible by B if the prime factorisation of B is completely contained in the prime factorisation of A — every prime in B must appear in A at least as many times. For example, 168 = 2×2×2×3×7 and 12 = 2×2×3. Since two 2s and one 3 are all in 168, 168 is divisible by 12 (168 = 12 × 14).
11Is the Class 6 Maths Chapter 5 Prime Time PDF free to download? Do I need to sign up?
Yes, the NCERT Ganita Prakash Class 6 Chapter 5 PDF is available free on our app and website with no sign-up required. The official NCERT PDF can also be downloaded from ncert.nic.in at no cost.
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