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Which of the following pairs are co-prime: (30, 45), (57, 85), (121, 1331), (343, 216)?
To determine co-primality, find the greatest common divisor (GCD): • (30, 45): Not co-prime, GCD = 15. • (57, 85): Co-prime, GCD = 1, as they share no factors other than 1. • (121, 1331): Not co-prime, GCD = 11. • (343, 216): Co-prime, GCD = 1, as no common factors exist. Pairs are co-prime only ifRead more
To determine co-primality, find the greatest common divisor (GCD):
• (30, 45): Not co-prime, GCD = 15.
• (57, 85): Co-prime, GCD = 1, as they share no factors other than 1.
• (121, 1331): Not co-prime, GCD = 11.
• (343, 216): Co-prime, GCD = 1, as no common factors exist.
Pairs are co-prime only if their GCD is 1, ensuring no shared 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. a) 225 and 27
The prime factorization of 225 is 3² x 5² and that of 27 is 3³. For divisibility, the prime factorization of the divisor must be included in the dividend’s factorization. Here, 27 has 3³, while 225 only has 3², making divisibility impossible. Thus, 225 is not divisible by 27 because the power of 3 iRead more
The prime factorization of 225 is 3² x 5² and that of 27 is 3³. For divisibility, the prime factorization of the divisor must be included in the dividend’s factorization. Here, 27 has 3³, while 225 only has 3², making divisibility impossible. Thus, 225 is not divisible by 27 because the power of 3 in 225’s factorization is insufficient to accommodate the full factorization of 27.
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. b) 96 and 24
The prime factorization of 96 is 2⁵ × 3, and that of 24 is 2³ ×3. Since all factors of 24 are present in 96’s factorization with equal or greater powers, 96 is divisible by 24. Dividing 96 by 24 confirms this: 96÷24 = 4 with no remainder. This demonstrates that the prime factors of 24 are fully inclRead more
The prime factorization of 96 is 2⁵ × 3, and that of 24 is 2³ ×3. Since all factors of 24 are present in 96’s factorization with equal or greater powers, 96 is divisible by 24. Dividing 96 by 24 confirms this: 96÷24 = 4 with no remainder. This demonstrates that the prime factors of 24 are fully included in those of 96, validating 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/
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/