Chapter 5: Prime TimeClass 6 Mathematics — summary, notes, extra questions & NCERT solutions

Summary

This chapter develops factors, multiples and prime numbers through games. The idli-vada game introduces common multiples of two numbers, and treasure-hunting jumps introduce common factors and divisors. A prime number has exactly two factors \u2014 1 and itself \u2014 so the first primes are \(2, 3, 5, 7, 11, 13, \dots\); numbers with more than two factors are composite, and 1 is neither prime nor composite. The Sieve of Eratosthenes is used to list all primes up to 100. Two numbers are co-prime if their only common factor is 1, for example 4 and 9. The chapter introduces prime factorisation: every number greater than 1 can be written as a product of primes in only one way apart from order, e.g. \(56 = 2 \times 2 \times 2 \times 7\). Prime factorisation is then used to test whether two numbers are co-prime and whether one number divides another. Finally, simple divisibility tests for 10, 5, 2, 4 and 8 are derived by looking at the last one, two or three digits. The chapter also explores perfect numbers, twin primes and prime puzzles.

Key terms

Extra questions & answers

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Let us now play the ‘idli-vada’ game with different pairs of numbers:

Which of the following could be the other number:

What jump size can reach both 15 and 30? There are multiple jump sizes possible. Try to find them all.

Look at the table below. What do you notice?

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Check if these pairs are safe:

Which of the following pairs of numbers are co-prime?

While playing the ‘idli-vada’ game with different number pairs, Anshu observed something interesting!

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