To find multiples of 40 between 310 and 410, divide the lower bound by 40 (310 ÷ 40 = 7.75) and round up to 8. Multiply 40 by 8 to get 320, the first multiple. Similarly, dividing the upper bound (410 ÷ 40 = 10.25) and rounding down to 10 gives 400 as the last multiple. The full sequence is 320, 360Read more
To find multiples of 40 between 310 and 410, divide the lower bound by 40 (310 ÷ 40 = 7.75) and round up to 8. Multiply 40 by 8 to get 320, the first multiple. Similarly, dividing the upper bound (410 ÷ 40 = 10.25) and rounding down to 10 gives 400 as the last multiple. The full sequence is 320, 360, and 400, as all are divisible by 40 and fall within the specified range.
The required number must meet three criteria: be less than 40, have 7 as a factor, and have a digit sum of 8. The multiples of 7 under 40 are 7, 14, 21, 28, and 35. Out of these, only 35 satisfies the digit sum condition (3 + 5 = 8). Its complete set of factors is 1, 5, 7, and 35. Thus, the answer iRead more
The required number must meet three criteria: be less than 40, have 7 as a factor, and have a digit sum of 8. The multiples of 7 under 40 are 7, 14, 21, 28, and 35. Out of these, only 35 satisfies the digit sum condition (3 + 5 = 8). Its complete set of factors is 1, 5, 7, and 35. Thus, the answer is 35, fulfilling all the stated conditions.
To solve, the number must be under 100, divisible by both 3 and 5, and its digits differ by 1. Numbers divisible by 3 and 5 have 15 as their least common multiple. Checking these, 15 fits perfectly, as its digits (1 and 5) meet the condition where one is exactly 1 more than the other. The factors ofRead more
To solve, the number must be under 100, divisible by both 3 and 5, and its digits differ by 1. Numbers divisible by 3 and 5 have 15 as their least common multiple. Checking these, 15 fits perfectly, as its digits (1 and 5) meet the condition where one is exactly 1 more than the other. The factors of 15 include 1, 3, 5, and 15, further verifying it meets all the criteria.
To determine the common factors of 20 and 28, list their factors. For 20, the factors are 1, 2, 4, 5, 10, and 20. For 28, the factors are 1, 2, 4, 7, 14, and 28. Comparing these, the common factors are 1, 2, and 4. These shared divisors show the numbers' overlap, with 4 being the greatest common divRead more
To determine the common factors of 20 and 28, list their factors. For 20, the factors are 1, 2, 4, 5, 10, and 20. For 28, the factors are 1, 2, 4, 7, 14, and 28. Comparing these, the common factors are 1, 2, and 4. These shared divisors show the numbers’ overlap, with 4 being the greatest common divisor (GCD) and thus the largest number that divides both evenly.
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.
Find all multiples of 40 that lie between 310 and 410.
To find multiples of 40 between 310 and 410, divide the lower bound by 40 (310 ÷ 40 = 7.75) and round up to 8. Multiply 40 by 8 to get 320, the first multiple. Similarly, dividing the upper bound (410 ÷ 40 = 10.25) and rounding down to 10 gives 400 as the last multiple. The full sequence is 320, 360Read more
To find multiples of 40 between 310 and 410, divide the lower bound by 40 (310 ÷ 40 = 7.75) and round up to 8. Multiply 40 by 8 to get 320, the first multiple. Similarly, dividing the upper bound (410 ÷ 40 = 10.25) and rounding down to 10 gives 400 as the last multiple. The full sequence is 320, 360, and 400, as all are divisible by 40 and fall within the specified range.
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Who am I? a) I am a number less than 40. One of my factors is 7. The sum of my digits is 8.
The required number must meet three criteria: be less than 40, have 7 as a factor, and have a digit sum of 8. The multiples of 7 under 40 are 7, 14, 21, 28, and 35. Out of these, only 35 satisfies the digit sum condition (3 + 5 = 8). Its complete set of factors is 1, 5, 7, and 35. Thus, the answer iRead more
The required number must meet three criteria: be less than 40, have 7 as a factor, and have a digit sum of 8. The multiples of 7 under 40 are 7, 14, 21, 28, and 35. Out of these, only 35 satisfies the digit sum condition (3 + 5 = 8). Its complete set of factors is 1, 5, 7, and 35. Thus, the answer is 35, fulfilling all the stated conditions.
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Who am I? b) I am a number less than 100. Two of my factors are 3 and 5. One of my digits is 1 more than the other.
To solve, the number must be under 100, divisible by both 3 and 5, and its digits differ by 1. Numbers divisible by 3 and 5 have 15 as their least common multiple. Checking these, 15 fits perfectly, as its digits (1 and 5) meet the condition where one is exactly 1 more than the other. The factors ofRead more
To solve, the number must be under 100, divisible by both 3 and 5, and its digits differ by 1. Numbers divisible by 3 and 5 have 15 as their least common multiple. Checking these, 15 fits perfectly, as its digits (1 and 5) meet the condition where one is exactly 1 more than the other. The factors of 15 include 1, 3, 5, and 15, further verifying it meets all the criteria.
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Find the common factors of: a) 20 and 28
To determine the common factors of 20 and 28, list their factors. For 20, the factors are 1, 2, 4, 5, 10, and 20. For 28, the factors are 1, 2, 4, 7, 14, and 28. Comparing these, the common factors are 1, 2, and 4. These shared divisors show the numbers' overlap, with 4 being the greatest common divRead more
To determine the common factors of 20 and 28, list their factors. For 20, the factors are 1, 2, 4, 5, 10, and 20. For 28, the factors are 1, 2, 4, 7, 14, and 28. Comparing these, the common factors are 1, 2, and 4. These shared divisors show the numbers’ overlap, with 4 being the greatest common divisor (GCD) and thus the largest number that divides both evenly.
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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.
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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.
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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.’
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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.
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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.
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