Class 6 Maths – Chapter: Prime Time
1. Introduction
- Prime numbers: Numbers greater than 1 that have only two factors: 1 and itself.
Example: 2, 3, 5, 7, 11… - Composite numbers: Numbers greater than 1 that have more than two factors.
Example: 4, 6, 8, 9… - 1 is neither prime nor composite.
2. Factors and Multiples
- Factor: A number that divides another number exactly.
Example: Factors of 12 → 1, 2, 3, 4, 6, 12 - Multiple: A number obtained by multiplying a given number by 1, 2, 3…
Example: Multiples of 4 → 4, 8, 12, 16…
3. Prime Factorization
- Prime factorization: Expressing a number as a product of prime numbers.
Example: 36 = 2 × 2 × 3 × 3 = 22×32
Method:
- Use factor trees to break down the number into prime factors.
4. HCF and LCM
- HCF (Highest Common Factor): The largest number that divides two or more numbers exactly.
Example: HCF of 12 and 18 → 6 - LCM (Least Common Multiple): The smallest number divisible by two or more numbers.
Example: LCM of 4 and 5 → 20
Methods:
- Listing method
- Prime factorization method
5. Co-prime Numbers
- Numbers whose HCF is 1 are called co-prime.
Example: 8 & 15, 9 & 28
6. Examples
Example 1 – Prime Factorization
- 48 → 2 × 2 × 2 × 2 × 3 → 24×3
Example 2 – HCF and LCM
- Numbers: 12 and 18
- Prime factorization: 12 = 2² × 3, 18 = 2 × 3²
- HCF = 2 × 3 = 6
- LCM = 2² × 3² = 36
Class 6 Maths – Prime Time (50 Mixed Questions)
Part A – Multiple Choice Questions (MCQs) – 15 Questions
- Which of the following is a prime number?
a) 9
b) 11
c) 15
d) 21 - HCF of 24 and 36 is:
a) 6
b) 12
c) 18
d) 24 - LCM of 5 and 6 is:
a) 11
b) 30
c) 60
d) 15 - 1 is:
a) Prime
b) Composite
c) Neither - Which pair is co-prime?
a) 12 & 18
b) 7 & 15
c) 8 & 16
d) 9 & 27 - Which of these is a composite number?
a) 2
b) 3
c) 9
d) 5 - Prime factorization of 36 is:
a) 2 × 3 × 6
b) 2² × 3²
c) 2 × 2 × 9
d) 3² × 6 - HCF of 15 and 25 is:
a) 5
b) 10
c) 15
d) 25 - LCM of 4 and 5 is:
a) 9
b) 20
c) 10
d) 25 - The smallest prime number is:
a) 0
b) 1
c) 2
d) 3 - A number divisible only by 1 and itself is called:
a) Composite
b) Prime
c) Co-prime
d) Factor - HCF of co-prime numbers is:
a) 0
b) 1
c) 2
d) It varies - Which of the following is NOT a prime number?
a) 2
b) 17
c) 21
d) 13 - 2 × 2 × 3 × 3 × 5 represents the prime factorization of:
a) 60
b) 90
c) 180
d) 120 - Which of the following pairs is co-prime?
a) 12 & 18
b) 8 & 15
c) 14 & 21
d) 9 & 27
Part B – Fill in the Blanks – 10 Questions
- Prime numbers have exactly __________ factors.
- Factors of 20 are __________.
- Multiples of 7 up to 35 are __________.
- 36 = __________ × __________ × __________
- HCF of 8 & 12 is __________.
- The number 1 is __________ prime nor composite.
- LCM is always __________ than or equal to HCF.
- Two numbers whose HCF is 1 are called __________ numbers.
- Prime factorization of 48 is __________.
- The first five prime numbers are __________.
Part C – True/False – 5 Questions
- 2 is the only even prime number. (True)
- 15 is a prime number. (False)
- Co-prime numbers have HCF 1. (True)
- 1 is a prime number. (False)
- LCM is always greater than or equal to HCF. (True)
Part D – Match the Following – 5 Questions
| Column A | Column B |
|---|---|
| 31. Prime number | a) 1 and itself only |
| 32. Composite number | b) More than 2 factors |
| 33. Co-prime numbers | c) HCF = 1 |
| 34. HCF | d) Highest common factor |
| 35. LCM | e) Least common multiple |
Part E – Short Answer / Problem Solving – 15 Questions
- Find HCF and LCM of 16 and 24.
- Express 60 as a product of prime factors.
- Find two numbers co-prime to 20.
- Find LCM of 4, 6, and 8.
- Prime factorize 84.
- HCF of 36 and 54 = ?
- LCM of 12 and 15 = ?
- Write all factors of 28.
- Write first ten multiples of 7.
- Find HCF and LCM of 18 and 24 using prime factorization.
- Determine whether 29 is prime or composite.
- Find the prime factorization of 100.
- Are 9 and 28 co-prime? Justify.
- Find LCM of 6, 8, and 12.
- Why is 1 neither prime nor composite?
Answers – Class 6 Maths: Prime Time
Part A – MCQs (Answers)
- b) 11
- a) 12
- b) 30
- c) Neither
- b) 7 & 15
- c) 9
- b) 2² × 3²
- a) 5
- b) 20
- c) 2
- b) Prime
- b) 1
- c) 21
- c) 180 (2 × 2 × 3 × 3 × 5 = 180)
- b) 8 & 15
Part B – Fill in the Blanks (Answers)
- 2
- 1, 2, 4, 5, 10, 20
- 7, 14, 21, 28, 35
- 2 × 2 × 3 × 3
- 4
- Neither
- Greater
- Co-prime
- 2 × 2 × 2 × 2 × 3 → 2⁴ × 3
- 2, 3, 5, 7, 11
Part C – True/False (Answers)
- True
- False
- True
- False
- True
Part D – Match the Following (Answers)
| Column A | Column B |
|---|---|
| 31. Prime number | a) 1 and itself only |
| 32. Composite number | b) More than 2 factors |
| 33. Co-prime numbers | c) HCF = 1 |
| 34. HCF | d) Highest common factor |
| 35. LCM | e) Least common multiple |
Part E – Short Answer / Problem Solving (Answers)
- HCF and LCM of 16 & 24
- Prime factorization: 16 = 2⁴, 24 = 2³ × 3
- HCF = 2³ = 8
- LCM = 2⁴ × 3 = 48
- Prime factorization of 60 → 2 × 2 × 3 × 5 = 2² × 3 × 5
- Two numbers co-prime to 20 → 3, 7 (HCF with 20 = 1)
- LCM of 4, 6, 8
- Prime factorization: 4 = 2², 6 = 2 × 3, 8 = 2³
- LCM = 2³ × 3 = 24
- Prime factorization of 84 → 2 × 2 × 3 × 7 = 2² × 3 × 7
- HCF of 36 & 54
- 36 = 2² × 3², 54 = 2 × 3³
- HCF = 2 × 3² = 18
- LCM of 12 & 15
- 12 = 2² × 3, 15 = 3 × 5
- LCM = 2² × 3 × 5 = 60
- Factors of 28 → 1, 2, 4, 7, 14, 28
- First 10 multiples of 7 → 7, 14, 21, 28, 35, 42, 49, 56, 63, 70
- HCF and LCM of 18 & 24
- 18 = 2 × 3², 24 = 2³ × 3
- HCF = 2 × 3 = 6
- LCM = 2³ × 3² = 72
- 29 → Prime number (divisible only by 1 and 29)
- Prime factorization of 100 → 2 × 2 × 5 × 5 = 2² × 5²
- Are 9 and 28 co-prime?
- HCF(9, 28) = 1 → Yes, co-prime
- LCM of 6, 8, 12
- Prime factorization: 6 = 2 × 3, 8 = 2³, 12 = 2² × 3
- LCM = 2³ × 3 = 24
- Why is 1 neither prime nor composite?
- Because prime numbers have exactly 2 factors, composite numbers have more than 2 factors, but 1 has only 1 factor.