Factors and multiples use the same multiplication facts, yet describe different relationships. For families exploring schools in Serangoon, one clear example can help a child stop swapping the words and start explaining which number divides which.
Yangzheng Primary School’s Mathematics page highlights mathematical problem solving, hands-on concept development and Math Games Day. The independent paper activity here connects that broad emphasis on understanding with a focused number relationship; it is not an official school task.
Use positive whole numbers throughout this activity. Paper dots or drawn rectangles are sufficient. The useful question is not just “What is the answer?” but “How does this multiplication sentence support your choice?”
eduKateSG · Neighbourhood education
Choose your next learning step
Start with an idea, work through an example, or try the final activity together.
Understand the idea · Explore the distinction · Practise and explain
Contents
Explore, practise and connect · Four chapters
CHAPTER 1 OF 4
1. Build factor pairs for twelve
Draw twelve dots in equal rows. One row of twelve, two rows of six, and three rows of four all use every dot. Record 1 × 12 = 12, 2 × 6 = 12 and 3 × 4 = 12.
The positive factors of 12 are 1, 2, 3, 4, 6 and 12. Each divides 12 exactly, leaving no remainder. Five is not a factor because twelve dots cannot be arranged into equal rows of five without leftover dots.
Turning a three-by-four arrangement gives four-by-three, but it does not introduce new factors. List each factor once. Checking pairs systematically helps the child avoid forgetting either 1 or the number itself.
CHAPTER 2 OF 4
2. Make multiples by multiplying
Now keep four dots in each group and change the number of groups. One group gives 4, two groups give 8, three give 12 and four give 16. These are the first four positive multiples of 4.
Factors of 12 answer “What divides 12 exactly?” Multiples of 4 answer “What results when 4 is multiplied by a whole number?” In this activity we list positive multiples; zero is also a multiple in the broader whole-number definition.
A factor list for a positive whole number is finite, while its positive multiples continue without end. Do not stop at the number merely because the factor exercise stopped there. For example, 20 and 24 are also multiples of 4.
CHAPTER 3 OF 4
3. Say the relationship both ways
Use 3 × 4 = 12 to complete two sentences: “3 is a factor of 12” and “12 is a multiple of 3”. Both are true. The reversed claim “12 is a factor of 3” is false in our positive-whole-number setting.
Try another pair: 5 and 20. Since 20 ÷ 5 = 4 exactly, 5 is a factor of 20 and 20 is a multiple of 5. Asking which number is being divided makes the direction explicit.
Challenge the shortcut “The smaller number is always a factor.” Six is smaller than twenty, but 20 ÷ 6 does not give a whole number. Size alone cannot establish the relationship; an exact division or multiplication fact must support it.
CHAPTER 4 OF 4
4. Sort, justify and check
Create cards numbered 2, 3, 4, 6, 8, 12 and 16. Sort them using two headings: Factors of 12 and Multiples of 4. Allow overlap because a number can satisfy both descriptions.
The factors are 2, 3, 4, 6 and 12. The multiples of 4 are 4, 8, 12 and 16. Four and twelve belong under both headings. The card set does not include every factor of 12 because it omits 1.
Ask the child to justify one overlapping card and one rejected choice. For 12: it divides itself exactly and equals 4 × 3. End with a new pair, such as 7 and 21, and let the child write both true relationship sentences independently.
Sources and scope
School information checked on 16 October 2026 (Singapore time): Yangzheng Primary School: Mathematics. Programmes may change. Family activities are independently written by eduKateSG, not official school tasks. This article does not imply school endorsement, rank schools or guarantee admission or learning results.
For more local learning connections, explore the neighbourhood school and family learning guide.