The factors of 35 are 1, 5, 7, and 35, while the factors of 50 are 1, 2, 5, 10, 25, and 50. Comparing these, the shared divisors are 1 and 5, making them the common factors. Among these, 5 is the greatest common divisor (GCD), the highest number dividing both 35 and 50 evenly. This shared factor undRead more
The factors of 35 are 1, 5, 7, and 35, while the factors of 50 are 1, 2, 5, 10, 25, and 50. Comparing these, the shared divisors are 1 and 5, making them the common factors. Among these, 5 is the greatest common divisor (GCD), the highest number dividing both 35 and 50 evenly. This shared factor underscores the relationship between these two numbers.
To find multiples of 25 that are not multiples of 50, list multiples of 25 (25, 50, 75, 100, 125, etc.) and exclude those divisible by 50 (50, 100, etc.). The remaining numbers include 25, 75, and 125, which satisfy the condition. Each of these is divisible by 25 but not by 50, as their divisibilityRead more
To find multiples of 25 that are not multiples of 50, list multiples of 25 (25, 50, 75, 100, 125, etc.) and exclude those divisible by 50 (50, 100, etc.). The remaining numbers include 25, 75, and 125, which satisfy the condition. Each of these is divisible by 25 but not by 50, as their divisibility excludes even multiples of 50.
Two numbers under 10 with an LCM exceeding 50 are 7 and 8. Their LCM is calculated using the formula LCM(a, b) = (a × b) ÷ GCD(a, b). Here, 7 and 8 have no common factors besides 1, making their GCD 1. The LCM is thus (7 × 8) ÷ 1 = 56. This exceeds 50, meeting the condition while ensuring the indiviRead more
Two numbers under 10 with an LCM exceeding 50 are 7 and 8. Their LCM is calculated using the formula LCM(a, b) = (a × b) ÷ GCD(a, b). Here, 7 and 8 have no common factors besides 1, making their GCD 1. The LCM is thus (7 × 8) ÷ 1 = 56. This exceeds 50, meeting the condition while ensuring the individual numbers are less than 10.
For ‘idli-vada’ to first occur after 50, the two numbers must have an LCM exceeding 50 but less than 60. Numbers under 10 with this property are 6 and 9, whose LCM is 54. The LCM is calculated as (6 × 9) ÷ 3 = 54, where 3 is their greatest common divisor (GCD). Thus, the first shared multiple afterRead more
For ‘idli-vada’ to first occur after 50, the two numbers must have an LCM exceeding 50 but less than 60. Numbers under 10 with this property are 6 and 9, whose LCM is 54. The LCM is calculated as (6 × 9) ÷ 3 = 54, where 3 is their greatest common divisor (GCD). Thus, the first shared multiple after 50 is 54, fulfilling the game’s condition for ‘idli-vada.’
To reach both treasures, the jump size must divide both 28 and 70. The factors of 28 are 1, 2, 4, 7, 14, and 28, and the factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70. The common factors are 1, 2, 7, and 14. Among these, 14 is the greatest common divisor (GCD), ensuring it is the smallest jump siRead more
To reach both treasures, the jump size must divide both 28 and 70. The factors of 28 are 1, 2, 4, 7, 14, and 28, and the factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70. The common factors are 1, 2, 7, and 14. Among these, 14 is the greatest common divisor (GCD), ensuring it is the smallest jump size that successfully lands on both numbers.
The least common multiple (LCM) of all numbers from 1 to 10 is 2520, found by considering their prime factorizations. To exclude 7, divide 2520 by 7, yielding 360. This number is divisible by all integers from 1 to 10 except 7, satisfying the condition. The prime factorization of 360 further confirmRead more
The least common multiple (LCM) of all numbers from 1 to 10 is 2520, found by considering their prime factorizations. To exclude 7, divide 2520 by 7, yielding 360. This number is divisible by all integers from 1 to 10 except 7, satisfying the condition. The prime factorization of 360 further confirms this: 360 = 2 × 2 × 2 × 3 × 3 × 5, excluding 7 as a factor.
To determine the smallest number that is a multiple of all numbers from 1 to 10, compute their least common multiple (LCM). Using prime factorizations, we find that 2, 3, 5, and 7 must be included with appropriate powers. The LCM is 2520, derived from 2³ × 3² × 5 × 7. This number is divisible by eveRead more
To determine the smallest number that is a multiple of all numbers from 1 to 10, compute their least common multiple (LCM). Using prime factorizations, we find that 2, 3, 5, and 7 must be included with appropriate powers. The LCM is 2520, derived from 2³ × 3² × 5 × 7. This number is divisible by every integer from 1 to 10, confirming it as the smallest common multiple for this range.
Between 21 and 30, the prime numbers are 23 and 29, totaling 2. These numbers have no divisors other than 1 and themselves. The remaining numbers (21, 22, 24, 25, 26, 27, 28, and 30) are composite, totaling 8. Composite numbers have additional divisors, like 24 (divisible by 2, 3, 4, 6, 8, and 12).Read more
Between 21 and 30, the prime numbers are 23 and 29, totaling 2. These numbers have no divisors other than 1 and themselves. The remaining numbers (21, 22, 24, 25, 26, 27, 28, and 30) are composite, totaling 8. Composite numbers have additional divisors, like 24 (divisible by 2, 3, 4, 6, 8, and 12). Together, primes and composites account for all integers within this interval.
Between 1 and 100, there are exactly 25 prime numbers. These numbers include 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. Each of these has only two divisors, 1 and itself. They are fundamental in mathematics, as they form the building blocks foRead more
Between 1 and 100, there are exactly 25 prime numbers. These numbers include 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. Each of these has only two divisors, 1 and itself. They are fundamental in mathematics, as they form the building blocks for all composite numbers through multiplication.
Among all integers, 2 is unique as the only even prime number. A prime number has exactly two divisors: 1 and itself. Any even number other than 2 is divisible by 2, making it composite rather than prime. For example, 4, 6, 8, and 10 all have additional divisors besides 1 and themselves, disqualifyiRead more
Among all integers, 2 is unique as the only even prime number. A prime number has exactly two divisors: 1 and itself. Any even number other than 2 is divisible by 2, making it composite rather than prime. For example, 4, 6, 8, and 10 all have additional divisors besides 1 and themselves, disqualifying them as primes. Hence, 2 is the sole even number meeting the prime number criteria.
Find the common factors of: b) 35 and 50
The factors of 35 are 1, 5, 7, and 35, while the factors of 50 are 1, 2, 5, 10, 25, and 50. Comparing these, the shared divisors are 1 and 5, making them the common factors. Among these, 5 is the greatest common divisor (GCD), the highest number dividing both 35 and 50 evenly. This shared factor undRead more
The factors of 35 are 1, 5, 7, and 35, while the factors of 50 are 1, 2, 5, 10, 25, and 50. Comparing these, the shared divisors are 1 and 5, making them the common factors. Among these, 5 is the greatest common divisor (GCD), the highest number dividing both 35 and 50 evenly. This shared factor underscores the relationship between these two numbers.
For more NCERT Solutions for Class 6 Math Chapter 5 Prime Time Extra Questions and Answer:
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Find three numbers that are multiples of 25 but not multiples of 50.
To find multiples of 25 that are not multiples of 50, list multiples of 25 (25, 50, 75, 100, 125, etc.) and exclude those divisible by 50 (50, 100, etc.). The remaining numbers include 25, 75, and 125, which satisfy the condition. Each of these is divisible by 25 but not by 50, as their divisibilityRead more
To find multiples of 25 that are not multiples of 50, list multiples of 25 (25, 50, 75, 100, 125, etc.) and exclude those divisible by 50 (50, 100, etc.). The remaining numbers include 25, 75, and 125, which satisfy the condition. Each of these is divisible by 25 but not by 50, as their divisibility excludes even multiples of 50.
For more NCERT Solutions for Class 6 Math Chapter 5 Prime Time Extra Questions and Answer:
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Find two numbers smaller than 10 such that their LCM exceeds 50.
Two numbers under 10 with an LCM exceeding 50 are 7 and 8. Their LCM is calculated using the formula LCM(a, b) = (a × b) ÷ GCD(a, b). Here, 7 and 8 have no common factors besides 1, making their GCD 1. The LCM is thus (7 × 8) ÷ 1 = 56. This exceeds 50, meeting the condition while ensuring the indiviRead more
Two numbers under 10 with an LCM exceeding 50 are 7 and 8. Their LCM is calculated using the formula LCM(a, b) = (a × b) ÷ GCD(a, b). Here, 7 and 8 have no common factors besides 1, making their GCD 1. The LCM is thus (7 × 8) ÷ 1 = 56. This exceeds 50, meeting the condition while ensuring the individual numbers are less than 10.
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Anshu and his friends play the idli-vada game with two numbers smaller than 10. The first time anybody says ‘idli-vada’ is after the number 50. What could these two numbers be?
For ‘idli-vada’ to first occur after 50, the two numbers must have an LCM exceeding 50 but less than 60. Numbers under 10 with this property are 6 and 9, whose LCM is 54. The LCM is calculated as (6 × 9) ÷ 3 = 54, where 3 is their greatest common divisor (GCD). Thus, the first shared multiple afterRead more
For ‘idli-vada’ to first occur after 50, the two numbers must have an LCM exceeding 50 but less than 60. Numbers under 10 with this property are 6 and 9, whose LCM is 54. The LCM is calculated as (6 × 9) ÷ 3 = 54, where 3 is their greatest common divisor (GCD). Thus, the first shared multiple after 50 is 54, fulfilling the game’s condition for ‘idli-vada.’
For more NCERT Solutions for Class 6 Math Chapter 5 Prime Time Extra Questions and Answer:
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What jump sizes will land on both treasures at 28 and 70?
To reach both treasures, the jump size must divide both 28 and 70. The factors of 28 are 1, 2, 4, 7, 14, and 28, and the factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70. The common factors are 1, 2, 7, and 14. Among these, 14 is the greatest common divisor (GCD), ensuring it is the smallest jump siRead more
To reach both treasures, the jump size must divide both 28 and 70. The factors of 28 are 1, 2, 4, 7, 14, and 28, and the factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70. The common factors are 1, 2, 7, and 14. Among these, 14 is the greatest common divisor (GCD), ensuring it is the smallest jump size that successfully lands on both numbers.
For more NCERT Solutions for Class 6 Math Chapter 5 Prime Time Extra Questions and Answer:
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Find the smallest number that is a multiple of all the numbers from 1 to 10 except for 7.
The least common multiple (LCM) of all numbers from 1 to 10 is 2520, found by considering their prime factorizations. To exclude 7, divide 2520 by 7, yielding 360. This number is divisible by all integers from 1 to 10 except 7, satisfying the condition. The prime factorization of 360 further confirmRead more
The least common multiple (LCM) of all numbers from 1 to 10 is 2520, found by considering their prime factorizations. To exclude 7, divide 2520 by 7, yielding 360. This number is divisible by all integers from 1 to 10 except 7, satisfying the condition. The prime factorization of 360 further confirms this: 360 = 2 × 2 × 2 × 3 × 3 × 5, excluding 7 as a factor.
For more NCERT Solutions for Class 6 Math Chapter 5 Prime Time Extra Questions and Answer:
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Find the smallest number that is a multiple of all the numbers from 1 to 10.
To determine the smallest number that is a multiple of all numbers from 1 to 10, compute their least common multiple (LCM). Using prime factorizations, we find that 2, 3, 5, and 7 must be included with appropriate powers. The LCM is 2520, derived from 2³ × 3² × 5 × 7. This number is divisible by eveRead more
To determine the smallest number that is a multiple of all numbers from 1 to 10, compute their least common multiple (LCM). Using prime factorizations, we find that 2, 3, 5, and 7 must be included with appropriate powers. The LCM is 2520, derived from 2³ × 3² × 5 × 7. This number is divisible by every integer from 1 to 10, confirming it as the smallest common multiple for this range.
For more NCERT Solutions for Class 6 Math Chapter 5 Prime Time Extra Questions and Answer:
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How many prime numbers are there from 21 to 30? How many composite numbers are there from 21 to 30?
Between 21 and 30, the prime numbers are 23 and 29, totaling 2. These numbers have no divisors other than 1 and themselves. The remaining numbers (21, 22, 24, 25, 26, 27, 28, and 30) are composite, totaling 8. Composite numbers have additional divisors, like 24 (divisible by 2, 3, 4, 6, 8, and 12).Read more
Between 21 and 30, the prime numbers are 23 and 29, totaling 2. These numbers have no divisors other than 1 and themselves. The remaining numbers (21, 22, 24, 25, 26, 27, 28, and 30) are composite, totaling 8. Composite numbers have additional divisors, like 24 (divisible by 2, 3, 4, 6, 8, and 12). Together, primes and composites account for all integers within this interval.
For more NCERT Solutions for Class 6 Math Chapter 5 Prime Time Extra Questions and Answer:
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How many prime numbers are there between 1 and 100?
Between 1 and 100, there are exactly 25 prime numbers. These numbers include 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. Each of these has only two divisors, 1 and itself. They are fundamental in mathematics, as they form the building blocks foRead more
Between 1 and 100, there are exactly 25 prime numbers. These numbers include 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. Each of these has only two divisors, 1 and itself. They are fundamental in mathematics, as they form the building blocks for all composite numbers through multiplication.
For more NCERT Solutions for Class 6 Math Chapter 5 Prime Time Extra Questions and Answer:
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Is there any even prime number other than 2?
Among all integers, 2 is unique as the only even prime number. A prime number has exactly two divisors: 1 and itself. Any even number other than 2 is divisible by 2, making it composite rather than prime. For example, 4, 6, 8, and 10 all have additional divisors besides 1 and themselves, disqualifyiRead more
Among all integers, 2 is unique as the only even prime number. A prime number has exactly two divisors: 1 and itself. Any even number other than 2 is divisible by 2, making it composite rather than prime. For example, 4, 6, 8, and 10 all have additional divisors besides 1 and themselves, disqualifying them as primes. Hence, 2 is the sole even number meeting the prime number criteria.
For more NCERT Solutions for Class 6 Math Chapter 5 Prime Time Extra Questions and Answer:
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