1️⃣ Introduction
This chapter helps us understand the relationship between factors and multiples. It explains how numbers are connected through multiplication and division.
2️⃣ Key Concepts
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A number can be multiplied to get another number.
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A number can be divided exactly by some numbers – these are called its factors.
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Every number has 1 and itself as factors.
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Even and Odd numbers have different kinds of factors.
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Prime numbers have exactly 2 factors.
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Composite numbers have more than 2 factors.
3️⃣ Important Definitions
| Term | Definition |
|---|---|
| Factor | A number that divides another number exactly. |
| Multiple | The result of multiplying a number by another. |
| Even Number | A number that ends in 0, 2, 4, 6, 8. |
| Odd Number | A number that ends in 1, 3, 5, 7, 9. |
| Prime Number | A number that has only 2 factors – 1 and itself. |
| Composite Number | A number that has more than 2 factors. |
✅ 1 is a factor of every number.
✅ Every number is a multiple of itself.
✅ 2 is the only even prime number.
✅ Multiples are infinite, but factors are limited.
✅ If a number ends in 0 or 5, it is divisible by 5.
✅ A number divisible by 2 and 3 is also divisible by 6.
5️⃣ Tables / Charts
Factors and Multiples Example Table:
| Number | Factors | First 5 Multiples |
|---|---|---|
| 6 | 1, 2, 3, 6 | 6, 12, 18, 24, 30 |
| 8 | 1, 2, 4, 8 | 8, 16, 24, 32, 40 |
| 10 | 1, 2, 5, 10 | 10, 20, 30, 40, 50 |
6️⃣ Solved Examples
🔹 Q1: Find the factors of 12.
👉 1, 2, 3, 4, 6, 12
🔹 Q2: Write the first 5 multiples of 7.
👉 7, 14, 21, 28, 35
🔹 Q3: Is 9 a factor of 81?
👉 Yes, because 81 ÷ 9 = 9
7️⃣ Activity Section
🟨 Fill in the Blanks
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The smallest multiple of 3 is ___.
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The number 2 is a factor of all ___ numbers.
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The number 15 is divisible by ___ and ___.
🟩 Match the Following
| A | B |
|---|---|
| 5 | 5, 10, 15, 20 |
| 2 | 2, 4, 6, 8 |
| 9 | 3, 9, 27, 81 |
🟥 True or False
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Every number is a factor of 1. (False)
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2 is a factor of all even numbers. (True)
🟦 One-Word Answers
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How many factors does 7 have? → ___
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Is 17 prime or composite? → ___
8️⃣ Short Q&A (Concept Check)
Q1: What are the factors of 18?
👉 1, 2, 3, 6, 9, 18
Q2: Is 16 a multiple of 4?
👉 Yes
Q3: Name two common multiples of 3 and 5.
👉 15 and 30
9️⃣ Practice Questions
🟢 MCQs
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Which is a multiple of 9?
a) 14 b) 18 c) 21 d) 20
✅ Answer: b) 18 -
What is the smallest factor of every number?
a) 0 b) 1 c) 2 d) the number itself
✅ Answer: b) 1
🟡 Short Answer
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Find the first 5 multiples of 6.
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Write the factors of 24.
🔵 Long Answer
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Write all the factors and first 5 multiples of 10.
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What is the difference between a factor and a multiple? Give examples.
🔟 Summary / Recap
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Factors divide a number exactly.
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Multiples are obtained by multiplying a number.
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1 is a universal factor.
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Prime numbers have only 2 factors.
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Factors are limited, multiples are infinite.
🔚 Important Points to Remember
⭐ Factor × Factor = Multiple
⭐ All numbers have at least two factors
⭐ Multiples of a number can be formed by skip counting
⭐ Use multiplication tables to find multiples easily