The prime factorization of 343 is 7³, indicating it is composed entirely of the prime number 7. Meanwhile, 17 is a prime number with no shared factors with 7. For divisibility, all prime factors of 17 must appear in 343’s factorization, which they do not. Hence, 343 is not divisible by 17, as theirRead more
The prime factorization of 343 is 7³, indicating it is composed entirely of the prime number 7. Meanwhile, 17 is a prime number with no shared factors with 7. For divisibility, all prime factors of 17 must appear in 343’s factorization, which they do not. Hence, 343 is not divisible by 17, as their factorization reveals no overlap or commonality in prime factors.
The prime factorization of 999 is 3³ x 37, and that of 99 is 3² × 11. For divisibility, the prime factors of 99 must appear in 999’s factorization. Here, 3² is present in 3³ and 11 divides evenly into 999. Performing the division confirms this: 999÷99=10. Thus, all factors of 99 are found in 999’s fRead more
The prime factorization of 999 is 3³ x 37, and that of 99 is 3² × 11. For divisibility, the prime factors of 99 must appear in 999’s factorization. Here, 3² is present in 3³ and 11 divides evenly into 999. Performing the division confirms this: 999÷99=10. Thus, all factors of 99 are found in 999’s factorization, verifying divisibility.
To check co-primality, find the prime factorization of both numbers. For 56, it is 2³ × 7 for 63, it is 3² ×7. The shared factor 7 makes their greatest common divisor (GCD) 7, indicating they are not co-prime. Co-prime numbers must have no common factors other than 1, which is not the case here dueRead more
To check co-primality, find the prime factorization of both numbers. For 56, it is 2³ × 7 for 63, it is 3² ×7. The shared factor 7 makes their greatest common divisor (GCD) 7, indicating they are not co-prime. Co-prime numbers must have no common factors other than 1, which is not the case here due to their overlap in the factor 7.
Guna’s statement is correct. By definition, co-prime numbers have no common factors other than 1. Prime numbers themselves have only two divisors: 1 and the number itself. Since two distinct prime numbers (e.g., 3 and 5 or 7 and 11) do not share any other factors, they are always co-prime. This holdRead more
Guna’s statement is correct. By definition, co-prime numbers have no common factors other than 1. Prime numbers themselves have only two divisors: 1 and the number itself. Since two distinct prime numbers (e.g., 3 and 5 or 7 and 11) do not share any other factors, they are always co-prime. This holds universally, as the lack of common factors between primes ensures their co-primality regardless of the primes chosen.
To find three primes under 30 whose product equals 1955, test combinations: • 5 × 13 = 65 • 65 × 29 = 1955 Thus, the primes are 5, 13, and 29. All are less than 30 and their multiplication verifies the result. Each number is prime, confirmed by divisibility tests, ensuring no factors other than 1 anRead more
To find three primes under 30 whose product equals 1955, test combinations:
• 5 × 13 = 65
• 65 × 29 = 1955
Thus, the primes are 5, 13, and 29. All are less than 30 and their multiplication verifies the result. Each number is prime, confirmed by divisibility tests, ensuring no factors other than 1 and themselves. The solution satisfies the problem’s conditions.
Is the first number divisible by the second? Use prime factorization. c) 343 and 17
The prime factorization of 343 is 7³, indicating it is composed entirely of the prime number 7. Meanwhile, 17 is a prime number with no shared factors with 7. For divisibility, all prime factors of 17 must appear in 343’s factorization, which they do not. Hence, 343 is not divisible by 17, as theirRead more
The prime factorization of 343 is 7³, indicating it is composed entirely of the prime number 7. Meanwhile, 17 is a prime number with no shared factors with 7. For divisibility, all prime factors of 17 must appear in 343’s factorization, which they do not. Hence, 343 is not divisible by 17, as their factorization reveals no overlap or commonality in prime factors.
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/
Is the first number divisible by the second? Use prime factorization. d) 999 and 99
The prime factorization of 999 is 3³ x 37, and that of 99 is 3² × 11. For divisibility, the prime factors of 99 must appear in 999’s factorization. Here, 3² is present in 3³ and 11 divides evenly into 999. Performing the division confirms this: 999÷99=10. Thus, all factors of 99 are found in 999’s fRead more
The prime factorization of 999 is 3³ x 37, and that of 99 is 3² × 11. For divisibility, the prime factors of 99 must appear in 999’s factorization. Here, 3² is present in 3³ and 11 divides evenly into 999. Performing the division confirms this: 999÷99=10. Thus, all factors of 99 are found in 999’s factorization, verifying divisibility.
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/
Are 56 and 63 co-prime? Use prime factorization to verify.
To check co-primality, find the prime factorization of both numbers. For 56, it is 2³ × 7 for 63, it is 3² ×7. The shared factor 7 makes their greatest common divisor (GCD) 7, indicating they are not co-prime. Co-prime numbers must have no common factors other than 1, which is not the case here dueRead more
To check co-primality, find the prime factorization of both numbers. For 56, it is 2³ × 7 for 63, it is 3² ×7. The shared factor 7 makes their greatest common divisor (GCD) 7, indicating they are not co-prime. Co-prime numbers must have no common factors other than 1, which is not the case here due to their overlap in the factor 7.
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/
Guna says, Any two prime numbers are co-prime. Is he right?
Guna’s statement is correct. By definition, co-prime numbers have no common factors other than 1. Prime numbers themselves have only two divisors: 1 and the number itself. Since two distinct prime numbers (e.g., 3 and 5 or 7 and 11) do not share any other factors, they are always co-prime. This holdRead more
Guna’s statement is correct. By definition, co-prime numbers have no common factors other than 1. Prime numbers themselves have only two divisors: 1 and the number itself. Since two distinct prime numbers (e.g., 3 and 5 or 7 and 11) do not share any other factors, they are always co-prime. This holds universally, as the lack of common factors between primes ensures their co-primality regardless of the primes chosen.
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/
Find three prime numbers, all less than 30, whose product is 1955.
To find three primes under 30 whose product equals 1955, test combinations: • 5 × 13 = 65 • 65 × 29 = 1955 Thus, the primes are 5, 13, and 29. All are less than 30 and their multiplication verifies the result. Each number is prime, confirmed by divisibility tests, ensuring no factors other than 1 anRead more
To find three primes under 30 whose product equals 1955, test combinations:
• 5 × 13 = 65
• 65 × 29 = 1955
Thus, the primes are 5, 13, and 29. All are less than 30 and their multiplication verifies the result. Each number is prime, confirmed by divisibility tests, ensuring no factors other than 1 and themselves. The solution satisfies the problem’s conditions.
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/