Chapter 2

Factors, Multiples and Primes

How whole numbers are built out of primes, and the two tools — HCF and LCM — that turn that structure into answers about tiles, timetables and fractions.

หลักสูตรแกนกลาง / สสวท.: จำนวนและพีชคณิต (Number and Algebra)เนื้อหาเดียวกับ ห.ร.ม. และ ค.ร.น. ในระดับประถมปลายถึง ม.1 ของไทย
Common Core (US): 6.NS, 4.OA
Cambridge: Lower Secondary Stage 7 — Number: integers, powers and roots

2.1 Factors and multiples

นิยาม

Factor

A number that divides into another with no remainder. The factors of $12$ are $1, 2, 3, 4, 6, 12$ .

นิยาม

Multiple

The result of multiplying a number by a whole number. The multiples of $12$ are $12, 24, 36, 48, \dots$ and there is no end to them.

เคล็ดลับ

Factors go into a number and there are finitely many; multiples come out of it and there are infinitely many. Students who mix the two usually have not noticed that one list stops and the other does not.

Listing every factor without missing one

1Work in pairs from the outside in: $1 \times 24$ , $2 \times 12$ , $3 \times 8$ , $4 \times 6$
2Stop when the two numbers in a pair meet or cross
3Every pair contributes two factors, unless the number is a perfect square

ตัวอย่าง

List all the factors of $36$

วิธีทำ

1. $1 \times 36$ , $2 \times 18$ , $3 \times 12$ , $4 \times 9$ , $6 \times 6$
2.The pair $6 \times 6$ contributes only one new factor

ตอบ $1, 2, 3, 4, 6, 9, 12, 18, 36$ — nine factors

📖 3 more sections of this chapter are being checked

The whole chapter is written; we read it back section by section before releasing it, because maths nobody has checked should not be on a public page. What is open is complete — nothing here is abridged.

Read it — now practise it

Generate a worksheet on this topic, or sit a timed mock paper.

Build a worksheet Practice arena