The big picture
Here are the eleven ideas, in order.
| Idea | Remember | Example |
|---|---|---|
| Primes inside | Keep breaking until nothing breaks. | 60 = 2 × 2 × 3 × 5 |
| A factor tree | Split any way. The ends do not change. | Ends: 2, 2, 3, 5 |
| Biggest shared factor | The largest number both factor lists share. | HCF(12, 18) = 6 |
| HCF from primes | Pair the two lists. Multiply what pairs. | 2 × 3 = 6 |
| Where counts meet | The first number on both lists of multiples. | LCM(12, 18) = 36 |
| LCM from primes | Pool the lists. Take the most of each piece. | 2 × 2 × 3 × 3 = 36 |
| Which one | Goes into both: HCF. Both go into it: LCM. | ribbon: HCF |
| Check it | Test 1: goes in. Test 2: nothing better exists. | HCF(12, 18) is not 9 |
| Co-prime pairs | Two numbers are co-prime when 1 is the only factor they share. | 14 and 15 |
| One division table | Stop when the two numbers in a row are co-prime. Multiply the divisors for the HCF. Multiply the divisors and the last row for the LCM. | 126, 198: HCF 18 |
| The product rule | HCF × LCM equals the product of the two numbers. | 12 × 180 = 36 × 60 |
Your textbook calls this Part II, Chapter 3, Finding Common Ground. Go and try its questions.
One habit helps every time. Write what each number is made of. Then a shared piece is easy to see.