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deepshikhasingh15
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G6 Multiples and Factors
Math quiz helps us to enhance brains neural network.
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1) Sticks of lengths 18 cm, 24 cm, and 30 cm are to be cut into equal-sized smaller sticks with no waste. What is the maximum length of each piece? How many pieces will we get from each stick?
Find the HCF of all stick lengths to get the longest piece possible.
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2) How many times does 2 appear in the prime factorization of 48?
48 = 2⁴ × 3 → 2 appears 4 times
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3) Which of the following is NOT a factor pair of 48?
3 × 16 = 48 ✔; 4 × 12 ✔; 5 × 9 = 45 ✘
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4) Which of these numbers has exactly 2 factors?
Prime numbers have exactly 2 factors → 13 is prime
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5) Find the least number which when divided by 16, 24, 36, and 45 leaves a remainder of 7 in each case.
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6) Find the smallest four-digit number that is divisible by 20, 25, and 30.
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7) The sum of two co-prime numbers is 11. How many such pairs are possible?
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8) Three ropes of lengths 36 m, 48 m, and 60 m are to be cut into equal lengths. What is the longest length that can be used to cut all ropes exactly?
HCF of 36, 48 and 60 is 12
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9) The least common multiple of two numbers is 56, and their highest common factor is 7. If one of the numbers is 28, what is the other number?
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10) If n is a prime number greater than 3, how many factors does 3n have?
Let n be 5, then the factors of 15 are 1, 3, 5 and 15. This means 15 has 4 factors. The same is true for other prime numbers greater than 3.
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11) A number ‘p’ is a common factor of 20 and 30. It is also a common multiple of 2 and 5. Another number ‘q’ is a common factor of 27 and 36. It is also a common multiple of 3 and 9. What is the value of p×q?
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12) A number ‘m’ is a common factor of 10 and 25. It is also a common multiple of 1 and 5. Another number ‘n’ is a common factor of 22 and 33. It is also a common multiple of 1 and 11. What is the value of m × n?
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13) A baker has 180 chocolate cookies and 150 vanilla cookies. What is the largest number of identical boxes he can make with no cookies left?
HCF(180, 150) = 30
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14) What is the largest 3-digit number that is divisible by both 10 and 15?
Largest 3-digit number divisible by LCM of 10 and 15.
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15) What is the smallest 3-digit number that is divisible by both 9 and 12?
LCM of 9 and 12 is 36; smallest 3-digit multiple of 36 is 108.
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16) Which of the following numbers can never be the last digit of an even number?
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17) The product of two numbers is 180, and their highest common factor is 6. If one of the numbers is 30, what is the least common multiple of the two numbers?
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18) What is the LCM of 24 and 36?
Prime factorization → 24 = 2³ × 3, 36 = 2² × 3² → LCM = 2³ × 3² = 72
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19) Which of the following is a factor pair of 36?
One correct pair: 6 × 6 = 36
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20) If the product of two numbers is 150 and their highest common factor is 5, what is their least common multiple?
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