Chapter 5: Prime Time
Some numbers can be split into equal groups in many ways; others refuse to split at all. In this chapter we play with multiples and factors, meet the prime numbers (the building blocks of all numbers), learn quick tricks to test divisibility, and end with puzzles that nobody has solved yet.
In this chapter you will
- find common multiples and common factors
- tell prime numbers from composite numbers, and find primes with a sieve
- spot co-prime numbers and break numbers into prime factors
- test divisibility by 2, 4, 5, 8 and 10 without dividing
Topics
- Common Multiples and Common Factors NCERT 5.1
Multiples: count in jumps (4, 8, 12 …). Factors: numbers that divide exactly (factors of 12: 1, 2, 3, 4, 6, 12).
- Prime Numbers NCERT 5.2
Prime: exactly two factors (1 and itself). Composite: more than two. 1 is neither.
- Co-prime Numbers NCERT 5.3
Co-prime: the only common factor is 1. They need not be prime (8 and 15).
- Prime Factorisation NCERT 5.4
Prime factorisation: write a number as a product of primes only (60 = 2 × 2 × 3 × 5).
- Divisibility Tests NCERT 5.5
10: last digit 0. 5: last digit 0 or 5. 2: last digit even.
- Fun with Numbers NCERT 5.6
Twin primes differ by 2 (11 and 13).
Key words
- Multiple
- what you get by counting in jumps of a number (3, 6, 9 …)
- Factor
- a number that divides another exactly
- Prime number
- a number with exactly two factors, 1 and itself
- Composite number
- a number with more than two factors
- Co-prime
- two numbers whose only common factor is 1
- Prime factorisation
- a number written as a product of primes only
Summary
- Common multiples appear in the multiple lists of both numbers; common factors appear in both factor lists.
- A prime has exactly two factors; a composite has more; 1 is neither. 2 is the only even prime.
- Co-prime numbers share no factor except 1, even when neither of them is prime.
- Every composite number is a product of primes in exactly one way (apart from order).
- Divisibility can be tested from the last digits: one digit for 2, 5 and 10, two for 4, three for 8.