Chapter 11: Finding Common Ground
Numbers, like people, have things in common. Two numbers may share a factor (something that divides both) or a multiple (something they both divide). Finding these common grounds helps us simplify fractions, schedule events, design tiles, and much more.
In this chapter you will sharpen your toolkit:
- Prime factorisation , breaking a number into a product of primes.
- HCF (Highest Common Factor) , the biggest number that divides both.
- LCM (Lowest Common Multiple) , the smallest number that both divide.
You will learn three ways to find HCF and LCM: listing, prime factorisation, and a fast algorithm called the Euclidean method (mostly for HCF).
Real-life uses pop up everywhere: planning when two buses next meet at a stop, cutting a strip into equal pieces, deciding the largest square tile that fits a rectangular floor. HCF and LCM are the tools of choice.
What's inside
- Factors and multiples , recap and the divisibility tests.
- Prime numbers and prime factorisation , the building blocks.
- HCF , Highest Common Factor , three methods.
- LCM , Lowest Common Multiple , three methods.
- HCF and LCM in real life , word problems.
Key results
| Term | Definition |
|---|---|
| Factor | A number that divides given number with no remainder |
| Multiple | A number obtained by multiplying given number by a positive integer |
| Prime | A whole number with exactly two factors: and itself |
| Prime factorisation | Express a number as product of primes |
| HCF | Largest number dividing all given numbers |
| LCM | Smallest non-zero number that is a multiple of all given numbers |
Key identity for two numbers: .
How to read this chapter
Always write out the prime factorisations side by side when computing HCF and LCM , the answers will jump out.