Chapter 5 — Prime Time

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.

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.

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.

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.

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.

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.

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.

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).

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.

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).

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.