To determine the smallest number with four distinct prime factors, use the smallest primes: 2,3,5, and 7. Their product, 2 × 3 × 5 × 7 = 210, is the minimal result. This ensures that all four factors are primes, and no other smaller combination meets the criteria. Including additional primes or largRead more
To determine the smallest number with four distinct prime factors, use the smallest primes: 2,3,5, and 7. Their product, 2 × 3 × 5 × 7 = 210, is the minimal result. This ensures that all four factors are primes, and no other smaller combination meets the criteria. Including additional primes or larger primes would result in a larger product, confirming 210 as the smallest valid number.
To verify co-primality, find the prime factorization: • 40 = 2³ × 5, with prime factors 2 and 5. • 231 = 3 × 7 × 11, with prime factors 3, 7, and 11. Since there are no overlapping prime factors between 40 and 231, their greatest common divisor (GCD) is 1. Therefore, they are co-prime, satisfying thRead more
To verify co-primality, find the prime factorization:
• 40 = 2³ × 5, with prime factors 2 and 5.
• 231 = 3 × 7 × 11, with prime factors 3, 7, and 11.
Since there are no overlapping prime factors between 40 and 231, their greatest common divisor (GCD) is 1. Therefore, they are co-prime, satisfying the condition of having no shared factors except for 1.
Prime factorization is the process of expressing a number as a product of prime numbers. For example, 24 = 2³ × 3. It breaks down the number into its smallest divisible prime components. To check divisibility, find the prime factorization: • 168 = 2³ × 3 × 712 • 12 = 2² × 3 All prime factors of 12 aRead more
Prime factorization is the process of expressing a number as a product of prime numbers. For example, 24 = 2³ × 3. It breaks down the number into its smallest divisible prime components.
To check divisibility, find the prime factorization:
• 168 = 2³ × 3 × 712
• 12 = 2² × 3
All prime factors of 12 are included in 168’s factorization, with 2² and 3 present. Dividing confirms this: 168 ÷ 12 = 14, with no remainder. Since 12’s prime factors are fully represented in 168’s decomposition, it is divisible by 12.
To determine divisibility, use prime factorizations: • 75 = 3 × 5² • 21 = 3 × 7 While both share the factor 3, 75 lacks the factor 7, which is required for divisibility. As a result, the prime factorization of 21 is not fully included in that of 75. Dividing confirms this: 75 ÷ 21 leaves a remainderRead more
To determine divisibility, use prime factorizations:
• 75 = 3 × 5²
• 21 = 3 × 7
While both share the factor 3, 75 lacks the factor 7, which is required for divisibility. As a result, the prime factorization of 21 is not fully included in that of 75. Dividing confirms this: 75 ÷ 21 leaves a remainder, proving that 75 is not divisible by 21.
Guna tested divisibility for 8 and 5 to conclude that 14560 is divisible by 2, 4, 5, 8, and 10. Divisibility by 8 ensures the number is divisible by 2 and 4, as 8 encompasses their factors. Similarly, divisibility by 5 guarantees divisibility by 10, since 10 = 2 × 5. These two tests are sufficient tRead more
Guna tested divisibility for 8 and 5 to conclude that 14560 is divisible by 2, 4, 5, 8, and 10. Divisibility by 8 ensures the number is divisible by 2 and 4, as 8 encompasses their factors. Similarly, divisibility by 5 guarantees divisibility by 10, since 10 = 2 × 5. These two tests are sufficient to confirm that the number is divisible by all five conditions without additional checks.
Four different prime numbers?
To determine the smallest number with four distinct prime factors, use the smallest primes: 2,3,5, and 7. Their product, 2 × 3 × 5 × 7 = 210, is the minimal result. This ensures that all four factors are primes, and no other smaller combination meets the criteria. Including additional primes or largRead more
To determine the smallest number with four distinct prime factors, use the smallest primes: 2,3,5, and 7. Their product, 2 × 3 × 5 × 7 = 210, is the minimal result. This ensures that all four factors are primes, and no other smaller combination meets the criteria. Including additional primes or larger primes would result in a larger product, confirming 210 as the smallest valid number.
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/
Use prime factorization to check if 40 and 231 are co-prime.
To verify co-primality, find the prime factorization: • 40 = 2³ × 5, with prime factors 2 and 5. • 231 = 3 × 7 × 11, with prime factors 3, 7, and 11. Since there are no overlapping prime factors between 40 and 231, their greatest common divisor (GCD) is 1. Therefore, they are co-prime, satisfying thRead more
To verify co-primality, find the prime factorization:
• 40 = 2³ × 5, with prime factors 2 and 5.
• 231 = 3 × 7 × 11, with prime factors 3, 7, and 11.
Since there are no overlapping prime factors between 40 and 231, their greatest common divisor (GCD) is 1. Therefore, they are co-prime, satisfying the condition of having no shared factors except for 1.
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/
Check if 168 is divisible by 12 using prime factorization.
Prime factorization is the process of expressing a number as a product of prime numbers. For example, 24 = 2³ × 3. It breaks down the number into its smallest divisible prime components. To check divisibility, find the prime factorization: • 168 = 2³ × 3 × 712 • 12 = 2² × 3 All prime factors of 12 aRead more
Prime factorization is the process of expressing a number as a product of prime numbers. For example, 24 = 2³ × 3. It breaks down the number into its smallest divisible prime components.
To check divisibility, find the prime factorization:
• 168 = 2³ × 3 × 712
• 12 = 2² × 3
All prime factors of 12 are included in 168’s factorization, with 2² and 3 present. Dividing confirms this: 168 ÷ 12 = 14, with no remainder. Since 12’s prime factors are fully represented in 168’s decomposition, it is divisible by 12.
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/
Check if 75 is divisible by 21 using prime factorization.
To determine divisibility, use prime factorizations: • 75 = 3 × 5² • 21 = 3 × 7 While both share the factor 3, 75 lacks the factor 7, which is required for divisibility. As a result, the prime factorization of 21 is not fully included in that of 75. Dividing confirms this: 75 ÷ 21 leaves a remainderRead more
To determine divisibility, use prime factorizations:
• 75 = 3 × 5²
• 21 = 3 × 7
While both share the factor 3, 75 lacks the factor 7, which is required for divisibility. As a result, the prime factorization of 21 is not fully included in that of 75. Dividing confirms this: 75 ÷ 21 leaves a remainder, proving that 75 is not divisible by 21.
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/
The teacher asked if 14560 is divisible by all of 2, 4, 5, 8, and 10. Guna checked for divisibility by only two of these numbers and declared it was divisible by all. What could those two numbers be?
Guna tested divisibility for 8 and 5 to conclude that 14560 is divisible by 2, 4, 5, 8, and 10. Divisibility by 8 ensures the number is divisible by 2 and 4, as 8 encompasses their factors. Similarly, divisibility by 5 guarantees divisibility by 10, since 10 = 2 × 5. These two tests are sufficient tRead more
Guna tested divisibility for 8 and 5 to conclude that 14560 is divisible by 2, 4, 5, 8, and 10. Divisibility by 8 ensures the number is divisible by 2 and 4, as 8 encompasses their factors. Similarly, divisibility by 5 guarantees divisibility by 10, since 10 = 2 × 5. These two tests are sufficient to confirm that the number is divisible by all five conditions without additional checks.
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/