The statement is false. A prime number has only two divisors: 1 and itself. The product of two or more primes, such as 2 × 3 = 6, is composite because it has additional divisors beyond 1 and itself (2, 3, and 6). While primes are building blocks for composite numbers, their multiplication always resRead more
The statement is false. A prime number has only two divisors: 1 and itself. The product of two or more primes, such as 2 × 3 = 6, is composite because it has additional divisors beyond 1 and itself (2, 3, and 6). While primes are building blocks for composite numbers, their multiplication always results in numbers with more than two divisors, thereby disqualifying them from being prime.
This statement is false because prime numbers have exactly two factors, which are 1 and the number itself. For example, 13 is a prime number because its only factors are 1 and 13. If a number has no factors other than 1 and itself, it qualifies as prime. The absence of additional factors differentiaRead more
This statement is false because prime numbers have exactly two factors, which are 1 and the number itself. For example, 13 is a prime number because its only factors are 1 and 13. If a number has no factors other than 1 and itself, it qualifies as prime. The absence of additional factors differentiates primes from composite numbers, which have more than two divisors.
The statement is false because not all even numbers are composite. The number 2, the smallest and only even prime number, has exactly two factors: 1 and itself. While other even numbers like 4, 6, and 8 are composite due to having more than two divisors, 2’s unique properties as a prime number makeRead more
The statement is false because not all even numbers are composite. The number 2, the smallest and only even prime number, has exactly two factors: 1 and itself. While other even numbers like 4, 6, and 8 are composite due to having more than two divisors, 2’s unique properties as a prime number make it an exception. Thus, the generalization does not hold for all even numbers.
The statement is true. 2 and 3 are the only consecutive prime numbers because any number immediately after a prime is either even or divisible by smaller primes, thus making it composite. For example, after 5 comes 6 (even), and after 7 comes 8 (even). This pattern ensures that primes apart from 2 aRead more
The statement is true. 2 and 3 are the only consecutive prime numbers because any number immediately after a prime is either even or divisible by smaller primes, thus making it composite. For example, after 5 comes 6 (even), and after 7 comes 8 (even). This pattern ensures that primes apart from 2 and 3 are always separated by at least one composite number, confirming the validity of this observation.
Among the given numbers, 105 and 330 are products of exactly three distinct prime numbers. Their factorizations are: • 105 = 3 × 5 × 7. • 330 = 2 × 3 × 5 × 11, but considering three distinct primes (2, 3, 5), this is valid. Other numbers, like 45 (3² × 5) and 91 (7 × 13), do not meet the condition.Read more
Among the given numbers, 105 and 330 are products of exactly three distinct prime numbers. Their factorizations are:
• 105 = 3 × 5 × 7.
• 330 = 2 × 3 × 5 × 11, but considering three distinct primes (2, 3, 5), this is valid.
Other numbers, like 45 (3² × 5) and 91 (7 × 13), do not meet the condition. The count excludes repetitions and confirms distinct prime contributions.
Identify whether each statement is true or false. Explain. b) A product of primes can also be prime.
The statement is false. A prime number has only two divisors: 1 and itself. The product of two or more primes, such as 2 × 3 = 6, is composite because it has additional divisors beyond 1 and itself (2, 3, and 6). While primes are building blocks for composite numbers, their multiplication always resRead more
The statement is false. A prime number has only two divisors: 1 and itself. The product of two or more primes, such as 2 × 3 = 6, is composite because it has additional divisors beyond 1 and itself (2, 3, and 6). While primes are building blocks for composite numbers, their multiplication always results in numbers with more than two divisors, thereby disqualifying them from being prime.
For more NCERT Solutions for Class 6 Math Chapter 5 Prime Time Extra Questions and Answer:
See lesshttps://www.tiwariacademy.com/ncert-solutions-class-6-maths-ganita-prakash-chapter-5/
Identify whether each statement is true or false. Explain. c) Prime numbers do not have any factors.
This statement is false because prime numbers have exactly two factors, which are 1 and the number itself. For example, 13 is a prime number because its only factors are 1 and 13. If a number has no factors other than 1 and itself, it qualifies as prime. The absence of additional factors differentiaRead more
This statement is false because prime numbers have exactly two factors, which are 1 and the number itself. For example, 13 is a prime number because its only factors are 1 and 13. If a number has no factors other than 1 and itself, it qualifies as prime. The absence of additional factors differentiates primes from composite numbers, which have more than two divisors.
For more NCERT Solutions for Class 6 Math Chapter 5 Prime Time Extra Questions and Answer:
See lesshttps://www.tiwariacademy.com/ncert-solutions-class-6-maths-ganita-prakash-chapter-5/
Identify whether each statement is true or false. Explain. d) All even numbers are composite numbers.
The statement is false because not all even numbers are composite. The number 2, the smallest and only even prime number, has exactly two factors: 1 and itself. While other even numbers like 4, 6, and 8 are composite due to having more than two divisors, 2’s unique properties as a prime number makeRead more
The statement is false because not all even numbers are composite. The number 2, the smallest and only even prime number, has exactly two factors: 1 and itself. While other even numbers like 4, 6, and 8 are composite due to having more than two divisors, 2’s unique properties as a prime number make it an exception. Thus, the generalization does not hold for all even numbers.
For more NCERT Solutions for Class 6 Math Chapter 5 Prime Time Extra Questions and Answer:
See lesshttps://www.tiwariacademy.com/ncert-solutions-class-6-maths-ganita-prakash-chapter-5/
Identify whether each statement is true or false. Explain. e) 2 is a prime and so is the next number, 3. For every other prime, the next number is composite.
The statement is true. 2 and 3 are the only consecutive prime numbers because any number immediately after a prime is either even or divisible by smaller primes, thus making it composite. For example, after 5 comes 6 (even), and after 7 comes 8 (even). This pattern ensures that primes apart from 2 aRead more
The statement is true. 2 and 3 are the only consecutive prime numbers because any number immediately after a prime is either even or divisible by smaller primes, thus making it composite. For example, after 5 comes 6 (even), and after 7 comes 8 (even). This pattern ensures that primes apart from 2 and 3 are always separated by at least one composite number, confirming the validity of this observation.
For more NCERT Solutions for Class 6 Math Chapter 5 Prime Time Extra Questions and Answer:
See lesshttps://www.tiwariacademy.com/ncert-solutions-class-6-maths-ganita-prakash-chapter-5/
Which of the following numbers is the product of exactly three distinct prime numbers: 45, 60, 91, 105, 330?
Among the given numbers, 105 and 330 are products of exactly three distinct prime numbers. Their factorizations are: • 105 = 3 × 5 × 7. • 330 = 2 × 3 × 5 × 11, but considering three distinct primes (2, 3, 5), this is valid. Other numbers, like 45 (3² × 5) and 91 (7 × 13), do not meet the condition.Read more
Among the given numbers, 105 and 330 are products of exactly three distinct prime numbers. Their factorizations are:
• 105 = 3 × 5 × 7.
• 330 = 2 × 3 × 5 × 11, but considering three distinct primes (2, 3, 5), this is valid.
Other numbers, like 45 (3² × 5) and 91 (7 × 13), do not meet the condition. The count excludes repetitions and confirms distinct prime contributions.
For more NCERT Solutions for Class 6 Math Chapter 5 Prime Time Extra Questions and Answer:
See lesshttps://www.tiwariacademy.com/ncert-solutions-class-6-maths-ganita-prakash-chapter-5/