1. Introduction
- Numbers are everywhere in daily life, and we can explore patterns, properties, and interesting facts using numbers.
- Number Play helps develop logical thinking, reasoning, and mathematical curiosity.
2. Factors and Multiples
Factors: Numbers that divide a given number exactly.
- Example: Factors of 12 → 1, 2, 3, 4, 6, 12
Multiples: Numbers obtained by multiplying a number with 1, 2, 3…
- Example: Multiples of 5 → 5, 10, 15, 20…
Special Terms:
- Prime numbers: Only two factors (1 and itself). Example: 2, 3, 5, 7…
- Composite numbers: More than two factors. Example: 4, 6, 8…
- Co-prime numbers: Two numbers with only 1 as common factor. Example: 8 & 15
3. Divisibility Rules
- 2: Last digit even (0,2,4,6,8)
- 3: Sum of digits divisible by 3
- 4: Last two digits divisible by 4
- 5: Last digit 0 or 5
- 6: Divisible by both 2 & 3
- 9: Sum of digits divisible by 9
- 10: Last digit 0
4. Prime Factorization
- Expressing a number as a product of its prime factors.
- Example: 36 = 2 × 2 × 3 × 3 = 2² × 3²
5. HCF and LCM
HCF (Highest Common Factor): Largest number that divides two or more numbers exactly.
- Example: HCF of 12 and 18 → 6
LCM (Least Common Multiple): Smallest number divisible by two or more numbers.
- Example: LCM of 4 and 5 → 20
Tips:
- Use prime factorization method for easy calculation.
6. Interesting Number Tricks
- All numbers divisible by 9 → sum of digits divisible by 9
- Numbers ending with 0 or 5 → divisible by 5
- Patterns in multiplication tables help recognize multiples easily
7. Magic Squares & Number Patterns
- Magic Square: Arrange numbers in a square so that the sum of each row, column, and diagonal is the same.
- Example:
8 1 6
3 5 7
4 9 2 8. Practice Questions
Part A – Multiple Choice Questions (MCQs) – 15 Questions
- Which of the following is a prime number?
a) 21
b) 17
c) 27
d) 33 - LCM of 4 and 6 is
a) 12
b) 24
c) 10
d) 6 - HCF of 18 and 24 is
a) 12
b) 6
c) 8
d) 18 - Which of these numbers is a composite number?
a) 2
b) 3
c) 9
d) 5 - Which of these pairs is co-prime?
a) 14 and 21
b) 8 and 15
c) 12 and 18
d) 6 and 9 - 1 is
a) Prime
b) Composite
c) Neither prime nor composite
d) Both prime and composite - Sum of first five multiples of 3 is
a) 30
b) 45
c) 40
d) 50 - Prime factorization of 36 is
a) 2 × 2 × 3 × 3
b) 2 × 3 × 6
c) 3 × 12
d) 2 × 18 - Which of the following numbers is divisible by 9?
a) 234
b) 325
c) 421
d) 156 - Which of the following is divisible by 5?
a) 42
b) 65
c) 38
d) 87 - LCM of two prime numbers is
a) 1
b) Their product
c) 0
d) 2 - HCF of two co-prime numbers is
a) 0
b) 1
c) Their sum
d) Their product - 72 ÷ 8 leaves a remainder of
a) 0
b) 1
c) 2
d) 3 - The number 1 has how many factors?
a) 1
b) 2
c) 0
d) Infinite - 14 × 15 is divisible by
a) 14 only
b) 15 only
c) 2, 3, 5, 7
d) None
Part B – Fill in the Blanks – 10 Questions
- Factors of 20 are __________.
- Multiples of 6 up to 36 are __________.
- Prime numbers between 10 and 20 are __________.
- Composite numbers between 10 and 20 are __________.
- 1 is __________ (prime/composite/neither).
- LCM of 5 and 10 is __________.
- HCF of 16 and 24 is __________.
- 45 is divisible by __________ and __________.
- 12 = 2 × 2 × 3; its prime factorization is __________.
- 2 and 9 are __________ numbers (co-prime/not co-prime).
Part C – True/False – 5 Questions
- 7 is a prime number. (True)
- 18 is a prime number. (False)
- LCM of 2 and 3 is 5. (False)
- All multiples of 10 end with 0. (True)
- HCF of 14 and 15 is 1. (True)
Part D – Match the Following – 5 Questions
| Column A | Column B |
|---|---|
| 31. Prime number | a) 2, 3, 5, 7 |
| 32. Composite number | b) 4, 6, 8, 9 |
| 33. Co-prime numbers | c) 8 & 15 |
| 34. LCM of 4 and 5 | d) 20 |
| 35. HCF of 18 and 24 | e) 6 |
Part E – Short Answer / Problem Solving – 15 Questions
- Find HCF of 12, 18, and 24.
- Find LCM of 8, 12, and 20.
- Express 60 as a product of prime factors.
- Check if 35 and 64 are co-prime.
- Find the sum of first five multiples of 7.
- Find the sum of first ten multiples of 5.
- Find HCF and LCM of 15 and 20.
- Check if 49 is divisible by 7.
- Find all factors of 28.
- Find all multiples of 9 up to 90.
- Find the smallest number divisible by both 12 and 18.
- Express 84 as a product of prime factors.
- Verify if 1 is prime or composite.
- Check whether 101 is a prime number.
- Find the LCM of 6, 8, and 12 using prime factorization.
Answers
Part A – MCQs (Answers)
- b) 17
- a) 12
- b) 6
- c) 9
- b) 8 and 15
- c) Neither prime nor composite
- b) 45 → (3+6+9+12+15=45)
- a) 2 × 2 × 3 × 3
- a) 234 → (2+3+4=9 divisible by 9)
- b) 65 → (last digit 5)
- b) Their product
- b) 1
- a) 0
- a) 1
- c) 2, 3, 5, 7
Part B – Fill in the Blanks (Answers)
- 1, 2, 4, 5, 10, 20
- 6, 12, 18, 24, 30, 36
- 11, 13, 17, 19
- 12, 14, 15, 16, 18, 20
- Neither prime nor composite
- 10
- 8
- 5 and 9
- 2 × 2 × 3
- Co-prime
Part C – True/False (Answers)
- True
- False
- False → LCM of 2 & 3 = 6
- True
- True
Part D – Match the Following (Answers)
| Column A | Answer (Column B) |
|---|---|
| 31. Prime number | a) 2, 3, 5, 7 |
| 32. Composite number | b) 4, 6, 8, 9 |
| 33. Co-prime numbers | c) 8 & 15 |
| 34. LCM of 4 and 5 | d) 20 |
| 35. HCF of 18 and 24 | e) 6 |
Part E – Short Answer / Problem Solving (Answers)
- HCF of 12, 18, 24 → 6
- LCM of 8, 12, 20 → 120
- 60 = 2 × 2 × 3 × 5 → 2² × 3 × 5
- 35 & 64 → HCF = 1 → Co-prime
- Sum of first five multiples of 7 → 7 + 14 + 21 + 28 + 35 = 105
- Sum of first ten multiples of 5 → 5 + 10 + … + 50 = 275
- HCF of 15 & 20 = 5, LCM = 60
- 49 ÷ 7 = 7 → divisible → Yes
- Factors of 28 → 1, 2, 4, 7, 14, 28
- Multiples of 9 up to 90 → 9, 18, 27, 36, 45, 54, 63, 72, 81, 90
- Smallest number divisible by 12 & 18 → LCM = 36
- 84 = 2 × 2 × 3 × 7 → 2² × 3 × 7
- 1 → Neither prime nor composite
- 101 → Prime (divisible only by 1 & 101)
- LCM of 6, 8, 12:
- Prime factorization: 6 = 2 × 3, 8 = 2³, 12 = 2² × 3
- LCM = 2³ × 3 = 24