🌟 QUICK CHAPTER NOTES
🔹 What are Factors?
A factor is a number that divides another number exactly (no remainder).
👉 Example:
Factors of 12 → 1, 2, 3, 4, 6, 12
🔹 Key Properties
- Every number has at least 2 factors → 1 and itself
- Factors are always less than or equal to the number
- Factors are finite
- Factors come in pairs
Example: 24 → (1,24), (2,12), (3,8), (4,6)
🔹 Common Factors
Factors that are common in two numbers
👉 Example:
12 → 1,2,3,4,6,12
18 → 1,2,3,6,9,18
Common → 1,2,3,6
🔹 Important Concepts
- Smallest factor of every number = 1
- Greatest factor of every number = the number itself
- A number with only 2 factors is a prime number
📝 EXERCISE 3.1 WORKSHEET
🔹 SECTION A (Very Short Answer)
- Write all factors of 18.
- Write all factors of 20.
- How many factors does 15 have?
- Write the smallest factor of any number.
- Write the greatest factor of 25.
- Is 1 a factor of every number?
- Is every number a factor of itself?
- Write all factors of 21.
- How many factors does 16 have?
- Write all factors of 13.
🔹 SECTION B (Short Answer)
- Write all factors of 24.
- Write all factors of 30.
- Find the number of factors of 36.
- Write the factors of 28.
- Write the factors of 50.
- Write all factors of 32.
- Write all factors of 45.
- Find the number of factors of 25.
- Write all factors of 40.
- Write all factors of 27.
🔹 SECTION C (Common Factors)
- Find common factors of 12 and 18.
- Find common factors of 10 and 15.
- Find common factors of 16 and 24.
- Find common factors of 14 and 21.
- Find common factors of 20 and 30.
- Find common factors of 9 and 27.
- Find common factors of 8 and 12.
- Find common factors of 15 and 25.
- Find common factors of 18 and 24.
- Find common factors of 6 and 9.
🔹 SECTION D (Factor Pairs)
- Write factor pairs of 24.
- Write factor pairs of 30.
- Write factor pairs of 36.
- Write factor pairs of 40.
- Write factor pairs of 48.
🔥 SECTION E – CASE-BASED QUESTIONS (NEW PATTERN)
📖 Case Study 1: Chocolate Boxes
Riya has 24 chocolates. She wants to arrange them in equal rows.
- List all possible numbers of rows she can make.
- How many total arrangements are possible?
- Which arrangement has equal rows and columns?
📖 Case Study 2: School Sports Teams
A teacher has 30 students and wants to divide them into equal groups.
- List all possible group sizes.
- If each group has 5 students, how many groups will be formed?
- Can she make groups of 7 students? Why?
📖 Case Study 3: Tile Arrangement
A floor has 36 tiles.
- List all possible rectangular arrangements.
- Which arrangement forms a square?
- How many total factor pairs does 36 have?
📖 Case Study 4: Number Puzzle
A number has factors: 1, 2, 4, 7, 14, 28
- Identify the number.
- How many factors does it have?
- Is it even or odd?
📖 Case Study 5: Factory Packaging
A factory packs 20 items into equal boxes.
- List all possible number of boxes.
- If each box has 4 items, how many boxes are needed?
- Which factor pair represents this situation?
✅ ANSWER KEY
SECTION A
- 1,2,3,6,9,18
- 1,2,4,5,10,20
- 4
- 1
- 25
- Yes
- Yes
- 1,3,7,21
- 5
- 1,13
SECTION B
- 1,2,3,4,6,8,12,24
- 1,2,3,5,6,10,15,30
- 9
- 1,2,4,7,14,28
- 1,2,5,10,25,50
- 1,2,4,8,16,32
- 1,3,5,9,15,45
- 3
- 1,2,4,5,8,10,20,40
- 1,3,9,27
SECTION C
- 1,2,3,6
- 1,5
- 1,2,4,8
- 1,7
- 1,2,5,10
- 1,3,9
- 1,2,4
- 1,5
- 1,2,3,6
- 1,3
SECTION D
- (1,24), (2,12), (3,8), (4,6)
- (1,30), (2,15), (3,10), (5,6)
- (1,36), (2,18), (3,12), (4,9), (6,6)
- (1,40), (2,20), (4,10), (5,8)
- (1,48), (2,24), (3,16), (4,12), (6,8)
SECTION E (Case-Based)
- 1,2,3,4,6,8,12,24
- 8
- 4 × 6 (closest rectangle), (perfect square only if equal → not possible except 1×24 not square)
- 1,2,3,5,6,10,15,30
- 6 groups
- No (30 not divisible by 7)
- (1,36), (2,18), (3,12), (4,9), (6,6)
- 6 × 6
- 5
- 28
- 6
- Even
- 1,2,4,5,10,20
- 5 boxes
- (4,5)