You will learn
- Say what a factor is.
- List all factors of a number up to 100.
- Test if one number is a factor of another.
- Use division to check.
Version 0.2 · expanded edition · expert review pending Standards alignment: pending verification. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- A factor divides a number exactly.
- Factors come in pairs.
- 1 and the number itself are always factors.
- Use division to test a factor.
Words to know
A number that divides another exactly.
Can be divided with no remainder.
The answer to a multiplication.
What is left over.
1. Discover: equal groups
12 mangoes can be shared equally among 1, 2, 3, 4, 6 or 12 children. Why not among 5?
2. Understand: factors
A factor of a number divides it exactly, with no remainder.
- Factors of 12: 1, 2, 3, 4, 6, 12.
- 5 is not a factor of 12 because 12 ÷ 5 = 2 remainder 2.
- 1 and the number itself are always factors.
To find all factors, test 1, 2, 3 … in order and stop when you meet a pair you already have.
Idea 1: What is a factor
4 is a factor of 12 because 12 ÷ 4 = 3 with no remainder.
Idea 2: Listing
Factors of 16: 1 × 16, 2 × 8, 4 × 4. So 1, 2, 4, 8, 16. Factors of 10: 1, 2, 5, 10.
Idea 3: Testing
Is 7 a factor of 28? 28 ÷ 7 = 4, so yes. Is 6 a factor of 20? 20 ÷ 6 = 3 r2, so no.
Why always 1? Every number divides exactly by 1 and by itself.
3. Worked examples
Example 1 (I show you): List
Factors of 10
- 1 × 10 and 2 × 5.
Answer: 1, 2, 5, 10
Example 2 (We do it together): Test
Is 7 a factor of 28?
- 28 ÷ 7 = 4.
Answer: Yes
Example 3 (You try): Test
Is 6 a factor of 20?
Show the steps and answer
- 20 ÷ 6 = 3 r2.
Answer: No
Did you know?
A number with exactly two factors is special. You will meet it soon.
Why this matters
Factors help us share things equally and simplify fractions.
4. Explore: factor hunt
You need paper and a pencil.
- Divide 12 by 1, 2, 3, 4, 5, 6.
- List those with no remainder.
- Do the same for 18.
- Check with multiplication.
Think about it: what did you notice?
12: 1, 2, 3, 4, 6, 12. 18: 1, 2, 3, 6, 9, 18.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- ___ is a factor of ___ because ___ ÷ ___ = ___.
- The factors of ___ are ___.
- ___ is not a factor because the remainder is ___.
- Always a factor: 1 and ___.
Guided practice
Question 1. Is 4 a factor of 12?
Yes, 12 ÷ 4 = 3.
Question 2. Is 5 a factor of 12?
No, remainder 2.
Question 3. Factors of 18?
1, 2, 3, 6, 9, 18.
Independent practice
Level 1: Start
- Factors of 10
- Is 7 a factor of 28? (yes/no)
- Factors of 16
- Is 6 a factor of 20? (yes/no)
- Always a factor of any number: 1 and ___
Level 2: Grow
- Factors of 14
- Is 9 a factor of 45?
- Is 4 a factor of 30?
Level 3: Stretch
- Factors of 28
- Is 12 a factor of 96?
- Ben says 6 is a factor of 16 because 16 is even. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
20 pupils form equal rows. List the possible row sizes.
Show a sample answer
1, 2, 4, 5, 10, 20.
Another one. 24 sweets are shared equally into groups with none left. List every possible group size.
Show a sample answer
1, 2, 3, 4, 6, 8, 12, 24
7. Common mistakes
Fix: Divide to check.
Fix: They are always factors.
Fix: A factor divides exactly.
8. Lesson summary and revision card
- I can say what a factor is.
- I can list factors of numbers up to 100.
- I can test if a number is a factor.
- I can use division to check.
9. Check and master
Answer all 14 questions. You will see feedback after each one.
Your result appears here after you answer every question.
10. Key takeaways
- Factors divide exactly.
- 1 and the number are factors.
- Check with division.
11. Next lesson
Next lesson: Factor pairs. Keep going with the next idea in this course.
Exam practice
These questions are written in the style of common school and international primary assessments. Try them on your own, without looking back. Then check your answers in the marking guide. The marks are shown in brackets.
- List the factors of 10. [2 marks]
- Is 7 a factor of 28? Explain. [2 marks]
- List the factors of 16. [3 marks]
- Is 6 a factor of 20? Explain. [2 marks]
- Ana says 5 is a factor of 12. Is she right? Explain. [3 marks]
Total: 12 marks.
Marking guide and model answers
- 1 × 10 and 2 × 5 [1]; 1, 2, 5, 10 [1]
- 7 × 4 = 28 [1]; yes [1]
- 1 × 16, 2 × 8, 4 × 4 [1]; 1, 2, 4, 8, 16 [1]; 4 listed once [1]
- 20 ÷ 6 = 3 r2 [1]; no [1]
- No [1]. 12 ÷ 5 = 2 r2 [1]. The remainder is not 0 [1].
Score guide: 11 to 12 = secure. 8 to 10 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.
Printable worksheet
- Factors of 10
- Is 7 a factor of 28? (yes/no)
- Factors of 16
- Is 6 a factor of 20? (yes/no)
- Always a factor: 1 and ___
- A factor of 12 is
- Which is not a factor of 12? 3, 4 or 5
- Factors of 10:
- Is 7 a factor of 28?
- Always a factor of any number:
Homework
Find all factors of your age and of 24.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Factors of 10 | 1, 2, 5, 10 | 2 |
| Is 7 a factor of 28? (yes/no) | yes | 2 |
| Factors of 16 | 1, 2, 4, 8, 16 | 2 |
| Is 6 a factor of 20? (yes/no) | no | 2 |
| Always a factor: 1 and ___ | itself | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 1, 2, 5, 10; 2 yes; 3 1, 2, 4, 8, 16; 4 no; 5 itself.
Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, 6 A, 7 B, 8 C, 9 A, 10 B, 11 C, 12 A, Challenge 1 C, Challenge 2 C.
Extra worksheet answers (items 6 onward): 6 4; 7 5; 8 1, 2, 5, 10; 9 yes; 10 1.
Independent practice answers. Level 1: 1 1, 2, 5, 10; 2 yes; 3 1, 2, 4, 8, 16; 4 no; 5 the number itself. Level 2: 1 1, 2, 7, 14; 2 yes; 3 no. Level 3: 1 1, 2, 4, 7, 14, 28; 2 yes, 12 × 8 = 96; 3 16 ÷ 6 = 2 r4, so 6 is not a factor..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Say what a factor is | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O2 List all factors of a number up to 100 | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O3 Test if one number is a factor of another | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O4 Use division to check | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
Proposed Courseversity thresholds for this page: Bronze = at least 8 of 12 core questions correct; Silver = all 12; Gold = all 12 plus both challenge questions. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Thinking 6 is a factor of 20 because 6 is less than 20. Divide to check.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Practise sharing objects equally.
- Guided practice: work through one example together and let the learner try the next one.
- Reassess: use the quiz again or the worksheet.
- Move on when the learner shows Silver-level evidence independently.
For parents and guardians
In this lesson your child finds the factors of numbers and tests if one number divides another exactly. You do not need to be good at mathematics to help.
- Share sweets into equal groups and list the sizes.
- Ask: does it divide exactly?
- Use arrays to show factor pairs.
- Ask “how do you know?” after each answer, and listen.
- Praise effort, not only right answers. Mistakes are how we learn.
- Ten to fifteen minutes a day is better than one long session.
Teacher package
1–5. Objectives, prerequisites, materials, preparation, duration
Lesson objectives. Learners will: say what a factor is; list all factors of a number up to 100; test if one number is a factor of another; use division to check.
Prerequisite knowledge. Grade 3 multiplication and division.
Materials. Counters (stones, seeds or bottle tops), paper, pencils, board or chalkboard. Low-resource options: use stones, seeds, sticks, bottle tops or drawings in the sand or on the board instead of printed materials.
Preparation. Gather the counters and draw the example pictures on the board before the lesson.
Suggested duration. 45–60 minutes. It can be split into two shorter sessions.
6–9. Teaching procedure, explanation notes, guided and independent activities
Introduction (5 min). Start with the Discover situation and let learners suggest ideas before you teach.
Explanation (10 min). Teach the Understand section with real objects first, then pictures, then symbols and words.
Guided activity (10 min). You need paper and a pencil. Learners follow the Explore steps in pairs.
Independent activity (10 min). Learners complete the independent practice and the worksheet.
Assessment and reflection (5 min). Ask each learner to say one thing they learned and how they know it.
Key questions. Does it divide with no remainder? Did I find every pair?
Teacher explanation notes. Use the concrete, pictorial, abstract order: real objects first, then pictures, then symbols and words. Return to real objects whenever a learner needs support.
10–12. Differentiation, formative assessment, common misconceptions
Support. Use real objects and work with a partner; say each step aloud together. Extension. Ask learners to make up their own example and explain it to a partner.
Formative assessment. Listen to learner explanations, ask “how do you know?”, and check the independent work.
Misconceptions. Thinking 6 is a factor of 20 because 6 is less than 20. Divide to check.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 12-mark exam practice scheme, the 10-mark scheme and all answers are in the answer sections above. Re-check every answer and the marking scheme before publication.
16–19. Remediation, enrichment, homework, teacher reflection
Remediation. Practise sharing objects equally. Enrichment. Invite learners to find or create three more examples at home or in the classroom and explain them. Homework. See above.
Teacher reflection. After teaching, record: which concepts learners understood; which misconceptions occurred; which activities worked; which learners need more practice; and what to improve next time.
Sources and standards
Alignment is pending verification and no external endorsement is claimed. Reference starting points named in the Courseversity standard: Common Core State Standards for Mathematics, Cambridge Primary and the IB Primary Years Programme. Specific standard codes will be added once checked against the official documents.
Research used to shape this lesson. Common Core 4.OA.B.4 (factors); Cambridge Primary Mathematics Stage 4 and 5 (factors and multiples). These sources informed the lesson; no official alignment is claimed.