Answer key Class 6 Mathematics – Chapter 5: Prime Time GANITA PRAKASH

🟢 Section A – Multiple Choice Questions (MCQs)

1. b) 31  

   Explanation: 31 has only two factors (1 and 31), making it prime. Others (21, 51, 91) are composite.

2. c) 2  

   Explanation: 2 is the smallest and only even prime number.

3. b) 1  

   Explanation: 1 has only one factor, so it’s neither prime nor composite.

4. b) 2² × 3²  

   Explanation: 36 = 2 × 2 × 3 × 3 = 2² × 3².

5. c) 12  

   Explanation: HCF of 24 (2³ × 3) and 36 (2² × 3²) is 2² × 3 = 12.

6. c) 20  

   Explanation: LCM of 4 and 5 is 4 × 5 = 20 (no common factors).

7. c) 14 and 15  

   Explanation: Co-prime pairs have HCF = 1. 14 (2 × 7) and 15 (3 × 5) share no common factors.

8. b) 2² × 3 × 7  

   Explanation: 84 = 2 × 2 × 3 × 7 = 2² × 3 × 7.

9. b) 2  

   Explanation: 2 is the only even prime number.

10. c) 20  

    Explanation: 20 is composite (factors: 1, 2, 4, 5, 10, 20). Others are prime.

11. b) 15  

    Explanation: LCM of 3 and 5 is 15.

12. a) 152 and c) 624  

    Explanation: Divisible by 4 if last two digits form a number divisible by 4 (52 → 52 ÷ 4 = 13; 24 → 24 ÷ 4 = 6).

13. a) 2, 7  

    Explanation: 56 = 2³ × 7 → Prime factors are 2 and 7.

14. b) 11 and 13  

    Explanation: Twin primes are pairs with a difference of 2 (e.g., 11 & 13).

15. b) Sum of its factors = twice the number  

    Explanation: 28’s factors (1, 2, 4, 7, 14, 28) sum to 56 = 2 × 28.

16. a) 30  

    Explanation: First three primes are 2, 3, 5 → Product = 2 × 3 × 5 = 30.

17. a) 125  

    Explanation: 125 ends with 5 (divisible by 5) but not 0 (not divisible by 10).

18. b) 1  

    Explanation: Co-prime numbers have HCF = 1.

19. a) 30  

    Explanation: 30 = 2 × 3 × 5 (three distinct primes). Others: 45 (3 × 3 × 5), 64 (2⁶), 49 (7 × 7).

20. c) 24  

    Explanation: LCM of 8 (2³) and 12 (2² × 3) is 2³ × 3 = 24.

 🟠 Section B – Assertion and Reasoning

1. a) Both A and R are true, and R explains A.  

   Explanation: 2 is prime (A) because it has only two factors (R).

2. a) Both A and R are true, and R explains A.  

   Explanation: 1 has only one factor (R), so it’s neither prime nor composite (A).

3. d) A is false but R is true.  

   Explanation: 91 = 7 × 13 (composite), but R correctly defines primes.

4. a) Both A and R are true, and R explains A.  

   Explanation: 15 and 16 are co-prime (A) as their HCF is 1 (R).

5. a) Both A and R are true, and R explains A.  

   Explanation: HCF of 20 and 25 is 5 (A), which is the largest common factor (R).

6. d) A is false but R is true.  

   Explanation: 2 is even but prime (A is false). R is true.

7. c) A is true but R is false.  

   Explanation: 13 is prime (A), but primes have exactly two factors (R is incorrect).

8. a) Both A and R are true, and R explains A.  

   Explanation: LCM of 9 and 12 is 36 (A), the smallest divisible by both (R).

9. a) Both A and R are true, and R explains A.  

   Explanation: 7 is the only prime between 6 and 8 (A) with two factors (R).

10. d) A is false but R is true.  

    Explanation: 2 is an even prime (A is false). R is true.

 🔵 Section C – True or False

1. True  

   Explanation: 2 is the only even prime.

2. False  

   Explanation: 1 is neither prime nor composite.

3. False  

   Explanation: 2 is even and prime.

4. True  

   Explanation: 57 = 3 × 19 (composite).

5. False  

   Explanation: Product of two primes is always composite (e.g., 2 × 3 = 6).

6. True  

   Explanation: Composite numbers have >2 factors.

7. True  

   Explanation: HCF of 9 and 12 is 3.

8. False  

   Explanation: LCM of 8 and 12 is 24, not 48.

9. True  

   Explanation: 100 ÷ 4 = 25 and 100 ÷ 25 = 4.

10. False  

    Explanation: 121 = 11 × 11 (composite).

 🟣 Section D – Short Answer Type I

1. 7, 14, 21, 28, 35  

2. 1, 2, 3, 4, 6, 8, 12, 24  

3. 3² × 5  

4. Yes, HCF = 1  

5. 4  

6. 18  

7. 31, 37, 41, 43, 47  

8. 101  

9. 2, 3, 5  

10. Yes, HCF = 1  

11. 101  

12. (3, 5), (5, 7), (11, 13), (17, 19)  

13. 12  

14. 60  

15. 2, 3, 5, 7, 11, 13, 17, 19  

 🟤 Section E – Short Answer Type II

1. HCF = 12, LCM = 72  

2. 2² × 3³  

3. Composite (221 = 13 × 17)  

4. 36  

5. Multiples of 9: 9, 18, 27, 36, 45; Multiples of 12: 12, 24, 36, 48, 60; Common multiple: 36  

6. HCF(13, 27) = 1 → Co-prime  

7. 2³ × 3²  

8. 16  

9. Yes, e.g., 14 & 15 (HCF = 1)  

10. 2² × 3 × 7  

 🔴 Section F – Long Answer Type

1. HCF = 4, LCM = 9696  

2. 2³ × 5³  

3. 72  

4. Primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97  

5. Sum of factors (1+2+4+7+14+28) = 56 = 2 × 28  

6. 13  

7. HCF = 10, LCM = 210  

8. A number is divisible by 4 if its last two digits form a number divisible by 4 (e.g., 124 → 24 ÷ 4 = 6).  

9. (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73)  

10. Prime: Only two factors (e.g., 5). Composite: >2 factors (e.g., 4). Co-prime: HCF = 1 (e.g., 8 & 9).  

 🟢 Section G – Case Based Questions

Case Study 1 – Idli-Vada Game  

1. b) 9, c) 12  

2. b) 20  

3. c) 15  

4. a) Common multiples of 3 and 5  

5. c) 15  

Case Study 2 – Jump Jackpot  

1. c) 10  

2. a) Factors of 24  

3. b) 2  

4. c) Common factors of 14 and 36  

5. b) 2  

Case Study 3 – Co-prime Safekeeping  

1. b) 4, 9  

2. a) No common factor except 1  

3. c) 35  

4. c) 81, 18  

Case Study 4 – Divisibility Tests  

1. c) 0 or 5  

2. b) 0, 2, 4, 6, 8  

3. a) 232  

4. a) Ends with 0  

Case Study 5 – Fun with Numbers  

1. d) 43  

2. a) It is a square  

3. b) Even and multiple of 4  

4. d) Both (a) and (b)