Chapter 3: Factors, multiples and primes
Some numbers break into smaller numbers and some do not. In this chapter you learn how to take a number apart, and what the pieces are good for.
The chapter problem
The two lighthouses. Two lighthouses flash regularly — one every 12 seconds, the other every 18 seconds. You see them flash together. How long until they do it again?
You can answer that by the end of the chapter, and you will see why it is the same kind of question as sharing 48 blue pens and 60 black pens into boxes with nothing left over. One question wants the lowest common multiple; the other wants the highest common factor. Telling them apart is most of the work.
By the end of this chapter you can
- list the factors and multiples of a number, and test whether one number divides another using the divisibility rules;
- write a number as a product of its prime factors;
- find the highest common factor and the lowest common multiple of two or more numbers, and say which one a problem is asking for.
Where it is used
Packing and sharing without waste, timetables and repeating events, and simplifying fractions — which is the next chapter.
Your turn to connect it
Where in your own week do two repeating things have to line up? Think of a bus and a train, two timers, or two people's work rotas. Write down one example and what "line up" means for it.
Sections
- 3.1 Factors, multiples and divisibility — factor pairs, the divisibility rules, squares and cubes
- 3.2 Prime numbers and prime factorisation — what makes a number prime, and taking a number apart into primes
- 3.3 The highest common factor and the lowest common multiple — the two questions, and telling them apart