NCERT Solutions for Class 6 Maths Chapter 5 - Prime Time Exercise 5.2

Exercise 5.2

1. We see that 2 is a prime and also an even number. Is there any other even prime? 

Ans: No, 2 is the only even prime number. All other even numbers can be divided by 2, so they are not prime.

2. Look at the list of primes till 100. What is the smallest difference between two successive primes? What is the largest difference? 

Ans: The smallest difference is 2 (for example, between 3 and 5). The largest difference is 8 (between 89 and 97).

3. Are there an equal number of primes occurring in every row in the table on the previous page? Which decades have the least number of primes? Which have the most number of primes?

Ans: No, there are not an equal number of primes in every decade.

• The decade with the least number of primes is 90-99 (only 2 primes: 97).

• The decade with the most number of primes is 1-10 (4 primes: 2, 3, 5, 7).

4. Which of the following numbers are prime: 23, 51, 37, 26? 

Ans: 23 and 37 are prime. 51 and 26 are not prime.

5. Write three pairs of prime numbers less than 20 whose sum is a multiple of 5. 

Ans:

•  2 and 3 (2 + 3 = 5)

• 3 and 7 (3 + 7 = 10)

• 7 and 13 (7 + 13 = 20)

6. The numbers 13 and 31 are prime numbers. Both these numbers have same digits 1 and 3. Find such pairs of prime numbers up to 100. 

Ans: 

• 13 and 31

• 17 and 71

• 37 and 73

7. Find seven consecutive composite numbers between 1 and 100. 

Ans: The seven consecutive composite numbers are 90, 91, 92, 93, 94, 95, 96.

8. Twin primes are pairs of primes having a difference of 2. For example, 3 and 5 are twin primes. So are 17 and 19. Find the other twin primes between 1 and 100.

Ans: The twin primes are:

• 3 and 5

• 5 and 7

• 11 and 13

• 17 and 19

• 29 and 31

• 41 and 43

• 59 and 61

• 71 and 73

9. Identify whether each statement is true or false. Explain. 

a. There is no prime number whose units digit is 4. 

b. A product of primes can also be prime.

c. Prime numbers do not have any factors. 

d. All even numbers are composite numbers. 

e. 2 is a prime and so is the next number, 3. For every other prime, the next number is composite. 

Ans: 

1. True, because no prime number ends with 4.

2. False, because multiplying two prime numbers gives a composite number.

3. False, prime numbers have exactly two factors: 1 and the number itself.

4. False, because 2 is an even number and a prime number.

5. True, the next number after any other prime is always composite.

10. Which of the following numbers is the product of exactly three distinct prime numbers: 45, 60, 91, 105, 330? 

Ans: 105 (105 = 3 × 5 × 7)

11. How many three-digit prime numbers can you make using each of 2, 4 and 5 once? 

Ans: You can make one prime number, which is 452.

12. Observe that 3 is a prime number, and 2 × 3 + 1 = 7 is also a prime. Are there other primes for which doubling and adding 1 gives another prime? Find at least five such examples.

Ans: 

• 3 → 2 × 3 + 1 = 7

• 5 → 2 × 5 + 1 = 11

• 11 → 2 × 11 + 1 = 23

• 13 → 2 × 13 + 1 = 27 (but 27 is not prime)

• 17 → 2 × 17 + 1 = 35 (but 35 is not prime)

• 7 → 2 × 7 + 1 = 15 (but 15 is not prime)

So, the valid examples are: 3, 5, and 11.

Benefits of NCERT Solutions for Class 6 Maths Chapter 5 Exercise 5.2 Prime Time

• Clear Understanding of Prime factorisation: The solutions offer step-by-step guidance on prime factorisation, making it easy for students to break down numbers into prime factors.

• Strengthens HCF Calculation Skills: Students learn various methods to find the highest common factor (HCF), building a strong foundation in number theory.

• Aligned with CBSE Syllabus: The solutions follow the CBSE Class 6 Maths syllabus, ensuring all important topics related to prime factorisation and HCF are covered.

• Boosts Problem-Solving Skills: With detailed explanations, these solutions enhance students' ability to tackle complex problems related to prime factorisation and HCF. 

• Exam-Oriented Preparation: The solutions provide ample practice, helping students prepare effectively for their exams with confidence.

• FREE PDF Access: Available for FREE PDF download, these solutions offer convenience for students to study and revise anytime. 

Class 6 Maths Chapter 5: Exercises Breakdown

Important Study Material Links for Class 6 Maths Chapter 5 - Prime Time

Conclusion

The NCERT Solutions for Class 6 Maths Chapter 5 Exercise 5.2, Prime Time, provide students with a thorough understanding of prime factorization and the highest common factor (HCF). With step-by-step explanations and clear guidance, these solutions simplify complex concepts, making learning easier and more effective. Aligned with the CBSE syllabus, they are a valuable tool for both regular practice and exam preparation. The FREE PDF download makes it convenient for students to access the solutions anytime, ensuring they build a strong foundation in number theory and problem-solving skills.

Chapter-Specific NCERT Solutions for Class 6 Maths

The chapter-wise NCERT Solutions for Class 6 Maths are given below. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

Related Important Links for Maths Class 6

Along with this, students can also download additional study materials provided by Vedantu for Maths Class 6.