Class 6 Mathematics Chapter 5 Prime Time

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Class 6 Mathematics Chapter 5 Prime Time

Test your knowledge of prime and composite numbers, divisibility rules, factors, multiples, prime factorization, and the highest common factor (HCF) and lowest common multiple (LCM) through this quiz. Get insights into your weaker areas and receive detailed explanations, key concept summaries, and video tutorials for a better grasp. Score 50% or more to earn a Certificate of Achievement by mail.

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Sub Topic: Common Multiples and Common Factors

1. Which of the following is a perfect number between 1 and 10?

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Sub Topic: Common Multiples and Common Factors

2. If a perfect number is divisible by 5, which of the following must also be true about it?

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Sub Topic: Playing the "Idli-Vada" game using multiples

3. (A) In the "Idli-Vada" game played with numbers 1 to 900, the number of times 'idli-vada' is said is equal to the number of common multiples of 3 and 5 within that range.
(R) The first common multiple of 3 and 5 is 15, and all subsequent common multiples are multiples of 15.

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Sub Topic: Playing the "Idli-Vada" game using multiples

4. In the "Idli-Vada" game played with numbers 4 and 6 for numbers from 1 to 90, how many times does "idli-vada" occur?

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Sub Topic: Finding common multiples (LCM) and common factors (HCF)

5. Three friends meet at a park every X days where X is the smallest number that leaves a remainder of 1 when divided by 5, 7, and 9 respectively. What is X?

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Sub Topic: Finding common multiples (LCM) and common factors (HCF)

6. (A) The HCF of 12 and 18 is 6.
(R) The largest number that divides both 12 and 18 without leaving a remainder is their HCF.

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Sub Topic: Jumpy and Grumpy’s treasure jump game

7. (A) If Jumpy chooses a jump size of 3, he can land on both 15 and 30 because 3 is a common factor of 15 and 30.
(R) A number is a common factor of two numbers if it divides both of them exactly.

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Sub Topic: Jumpy and Grumpy’s treasure jump game

8. In a special version of the game, Jumpy must use prime number jump sizes only. For treasures at 77 and 121, which of these prime jump sizes would work for both?

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Sub Topic: Introduction to factors and multiples

9. Which of the following pairs of numbers are co-prime?

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Sub Topic: Introduction to factors and multiples

10. (A) 250 is divisible by 10.
(R) Numbers ending with '0' are divisible by 10.

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Sub Topic: Games and visualizations using number grids

11. Grumpy places a treasure on the number 72. Which jump size will NOT allow Jumpy to land exactly on the treasure in the Jump Jackpot game?

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Sub Topic: Games and visualizations using number grids

12. What are all the factors of 24?

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Sub Topic: Prime Numbers

13. (A) The number 7 is a prime number.
(R) The number 7 has only two factors, 1 and itself.

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Sub Topic: Prime Numbers

14. Which of the following numbers will remain uncrossed after applying the Sieve of Eratosthenes up to 50?

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Sub Topic: Understanding prime and composite numbers

15. Which number should be circled next in the Sieve of Eratosthenes after crossing out multiples of 2 and 3?

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Sub Topic: Understanding prime and composite numbers

16. Using the Sieve of Eratosthenes, how many consecutive composite numbers exist between two primes in the range from 1 to 100?

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Sub Topic: Rectangular arrangements to visualize factors

17. If a number has more than two rectangular arrangements, what type of number is it?

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Sub Topic: Rectangular arrangements to visualize factors

18. (A) The number 15 can be arranged in exactly two different rectangular arrangements.
(R) A composite number has more than two distinct factors.

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Sub Topic: Listing primes up to 100 using the Sieve of Eratosthenes

19. Which pair represents twin primes among the following options?

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Sub Topic: Listing primes up to 100 using the Sieve of Eratosthenes

20. (A) The number 1 is neither prime nor composite.
(R) The Sieve of Eratosthenes starts by crossing out 1 as it does not fit the definition of a prime or composite number.

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Sub Topic: Composite numbers

21. (A) The number 18 is a composite number because it has more than two factors.
(R) A composite number can always be expressed as a product of prime numbers.

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Sub Topic: Composite numbers

22. Which pair of numbers is co-prime?

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Sub Topic: Perfect numbers

23. (A) The number 6 is a perfect number.
(R) The sum of all factors of 6 equals twice the number itself.

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Sub Topic: Perfect numbers

24. Which statement about perfect numbers is true?

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Sub Topic: Twin primes

25. (A) The pair $(11, 13)$ are twin primes because they differ by $2$ and both are prime numbers.
(R) Twin primes are pairs of prime numbers that have a difference of exactly $2$.

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Sub Topic: Twin primes

26. Why can't an even number be part of a twin prime pair (other than 2)?

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Sub Topic: Prime pairs with special properties

27. If $p$ is a prime number, for which value of $p$ does $2 \times p + 1$ also result in a prime?

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Sub Topic: Prime pairs with special properties

28. Find which of the following pairs of prime numbers are digit reversals of each other.

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Sub Topic: True or false reasoning about properties of primes

29. (A) 2 is the only even prime number.
(R) All other even numbers greater than 2 are divisible by 2, hence not prime.

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Sub Topic: True or false reasoning about properties of primes

30. Consider the process of applying the Sieve of Eratosthenes to find all prime numbers up to 100. Which of the following statements about the numbers remaining after each step is correct?

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Sub Topic: Co-prime Numbers for Safekeeping Treasures

31. Grumpy wants to place treasures on two numbers so that Jumpy cannot reach both with any jump size greater than 1. Which of these pairs should he choose?

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Sub Topic: Co-prime Numbers for Safekeeping Treasures

32. If two numbers are co-prime, then what must be true about them?

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Sub Topic: Definition of co-prime numbers (no common factor other than 1)

33. In a thread art activity with 20 pegs, which thread-gap will ensure the thread ties every peg?

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Sub Topic: Definition of co-prime numbers (no common factor other than 1)

34. Which of the following pairs of numbers are co-prime?

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Sub Topic: Applying this concept to treasure game strategies

35. Jumpy can only use jump sizes greater than 1. Grumpy wants to place treasures on two numbers such that at least three different jump sizes (greater than 1) allow reaching both treasures. Which pair should Grumpy choose?

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Sub Topic: Applying this concept to treasure game strategies

36. (A) Placing treasures on two co-prime numbers makes them safe because Jumpy cannot reach both with any jump size other than 1.
(R) Two numbers are co-prime if their greatest common divisor (GCD) is 1, and a jump size must be a common divisor of both numbers to reach them.

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Sub Topic: Examples of co-prime pairs

37. Which of the following pairs is co-prime?

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Sub Topic: Examples of co-prime pairs

38. (A) The pair (49, 121) is co-prime because both numbers are perfect squares of prime numbers.
(R) Two numbers that are perfect squares of distinct primes do not share any common prime factors other than 1.

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Sub Topic: Relationship between co-primes and LCM

39. (A) The LCM of two co-prime numbers is always equal to their product.
(R) Co-prime numbers have no common prime factors other than 1.

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Sub Topic: Relationship between co-primes and LCM

40. Two numbers $a$ and $b$ are co-prime. Which of the following statements is always true for these two numbers?

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Sub Topic: Visualizing co-primes using thread art

41. Consider two numbers whose prime factorisations are $a = 2^3 \times 5^2 \times 7$ and $b = 3^4 \times 11^2$. Which of the following statements is true about $a$ and $b$?

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Sub Topic: Visualizing co-primes using thread art

42. In thread art, if a circle has 12 pegs and the thread-gap is 4, will the thread tie every peg?

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Sub Topic: Prime Factorisation

43. Which pair of numbers are co-prime?

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Sub Topic: Prime Factorisation

44. What is the prime factorisation of 30?

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Sub Topic: Breaking down numbers into products of prime factors

45. Without multiplying first, what is the prime factorisation of $108 \times 75$?

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Sub Topic: Breaking down numbers into products of prime factors

46. (A) The prime factorisation of 60 is $2 \times 2 \times 3 \times 5$.
(R) Every composite number has a unique prime factorisation, regardless of the order of factors.

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Sub Topic: Systematic method for factorisation

47. What is the prime factorisation of the number 72?

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Sub Topic: Systematic method for factorisation

48. A teacher writes the prime factorisations of two numbers on the board: $A = 2^4 \times 3^2 \times 5$ and $B = 2^2 \times 3^3 \times 7$. What is the greatest common divisor (GCD) of A and B?

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Sub Topic: Prime factorisation of products

49. (A) The prime factorisation of $360$ includes the prime factor $5$.

(R) The number $360$ is divisible by $10$, and $10 = 2 \times 5$.

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Sub Topic: Prime factorisation of products

50. (A) The prime factorisation of $72$ is $2^3 \times 3^2$.
(R) The prime factorisation of $12$ is $2^2 \times 3$ and the prime factorisation of $6$ is $2 \times 3$, so multiplying them gives $2^3 \times 3^2$.

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Sub Topic: Uniqueness of prime factorisation (order doesn’t matter)

51. (A) The prime factorisation of 30 is $2 \times 3 \times 5$ and it remains the same regardless of the order of factors.
(R) The uniqueness of prime factorisation states that every number greater than 1 has a unique prime factorisation, except for the order of factors.

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Sub Topic: Uniqueness of prime factorisation (order doesn’t matter)

52. How many unique sets of prime factors does the number 36 have, ignoring the order of multiplication?

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Sub Topic: Use of prime factorisation to:

53. Are 45 and 32 co-prime?

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Sub Topic: Use of prime factorisation to:

54. (A) The numbers 105 and 121 are co-prime because they have no common prime factors.
(R) Two numbers are co-prime if their greatest common divisor (GCD) is 1.

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Sub Topic: Check co-primeness

55. Two numbers, $m$ and $n$, have the following prime factorisations: $m = 2^3 \times 5 \times 7^2$ and $n = 3^2 \times 11 \times 13$. Are $m$ and $n$ co-prime?

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Sub Topic: Check co-primeness

56. Guna says, "Any two prime numbers are co-prime." Is this statement always true?

57 / 100

Sub Topic: Check divisibility

57. Which pair shows that the first number is divisible by the second?

58 / 100

Sub Topic: Check divisibility

58. (A) The number $120$ is divisible by $15$ because
(R) All prime factors of $15$ are included in the prime factorisation of $120$.

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Sub Topic: Prime factorisation of a product of two numbers

59. A number N has a prime factorisation of $2^3 \times 3^2 \times 5$. Another number M is obtained by multiplying N with an unknown number X such that the prime factorisation of M becomes $2^4 \times 3^3 \times 5^2 \times 7$. What is the smallest possible positive integer value of X?

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Sub Topic: Prime factorisation of a product of two numbers

60. (A) If the prime factorisation of a number $N$ contains all the prime factors of another number $M$, then $N$ is divisible by $M$.
(R) The prime factorisation of the product of two numbers includes all the prime factors of both numbers combined.

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Sub Topic: Using prime factorisation to check if two numbers are co-prime

61. Using prime factorisation, determine if 15 and 28 are co-prime.

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Sub Topic: Using prime factorisation to check if two numbers are co-prime

62. Are 63 and 92 co-prime?

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Sub Topic: Using prime factorisation to check if one number is divisible by another

63. (A) The number 36 is divisible by 6.
(R) The prime factorisation of 6 ($2 \times 3$) is included in the prime factorisation of 36 ($2 \times 2 \times 3 \times 3$).

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Sub Topic: Using prime factorisation to check if one number is divisible by another

64. Is $392$ divisible by $28$?

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Sub Topic: Divisibility Tests

65. Which of the following numbers is divisible by 10?

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Sub Topic: Divisibility Tests

66. Which of the following statements is always true for numbers divisible by both 2 and 5?

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Sub Topic: Divisibility by 10, 5, 2, 4, 8

67. Which of the following numbers is divisible by 4?

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Sub Topic: Divisibility by 10, 5, 2, 4, 8

68. A teacher writes two numbers on the board: one divisible by 5 but not 10, and another divisible by 10. She asks for the sum of these numbers. Under what condition is the sum divisible by 10?

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Sub Topic: Identifying patterns using last digits

69. (A) The number 7530 is divisible by both 10 and 5.
(R) A number ending with '0' is divisible by both 5 and 10.

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Sub Topic: Identifying patterns using last digits

70. Which of the following numbers is divisible by 2?

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Sub Topic: Using divisibility rules to simplify calculations

71. Which of the following numbers is NOT divisible by 10?

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Sub Topic: Using divisibility rules to simplify calculations

72. (A) The number 572 is divisible by 2.
(R) A number that ends with an even digit (0, 2, 4, 6, or 8) is divisible by 2.

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Sub Topic: Exploring palindromes and leap years through divisibility

73. The number 14560 is divisible by which pair of numbers from 2, 4, 5, 8, and 10 such that checking these ensures divisibility by all others?

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Sub Topic: Exploring palindromes and leap years through divisibility

74. What is the smallest 4-digit palindrome divisible by 4?

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Sub Topic: Exercises to find remainders and apply logic

75. What is the remainder when 572 is divided by 10?

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Sub Topic: Exercises to find remainders and apply logic

76. Which pair of divisibility tests can confirm that a number is divisible by 2, 4, 5, 8, and 10 without checking all individually?

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Sub Topic: Fun with Numbers

77. Given the numbers 3, 8, 11, and 24, which of the following statements correctly identifies a unique special property of one number compared to the others?

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Sub Topic: Fun with Numbers

78. In the set of numbers 9, 16, 25, 43, which number is special because it is the only prime number?

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Sub Topic: Fun with Numbers

79. Which of the following numbers is special in the set \{5, 7, 12, 35\} based on divisibility by prime numbers?

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Sub Topic: Special numbers in sets (prime, square, multiples)

80. Which of the following pairs of numbers are co-prime and both numbers in the pair are also prime numbers?

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Sub Topic: Special numbers in sets (prime, square, multiples)

81. A number is perfect if the sum of its proper factors (excluding itself) equals the number. Which of the following is a perfect number and also a square number?

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Sub Topic: Special numbers in sets (prime, square, multiples)

82. (A) The number 25 is special because it is the only multiple of 5 among the numbers 9, 16, 25, and 43.
(R) Among the numbers 9, 16, 25, and 43, only 25 has 5 as one of its factors.

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Sub Topic: Puzzles involving:

83. (A) The number 127 is a prime number.
(R) 127 has exactly two distinct positive divisors, 1 and itself.

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Sub Topic: Puzzles involving:

84. A perfect number is one where the sum of all its factors equals twice the number. Which of the following numbers is a perfect number between 1 and 10?

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Sub Topic: Puzzles involving:

85. (A) The number 28 is a perfect number.
(R) A number is perfect if the sum of its factors equals twice the number.

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Sub Topic: Prime puzzles (grid-based)

86. (A) In a 3x3 prime puzzle grid, if the row product for the first row is 30, then the primes used must include at least one 2, one 3, and one 5.
(R) The number 30 can be factorized into primes as $2 \times 3 \times 5$.

87 / 100

Sub Topic: Prime puzzles (grid-based)

87. In solving a prime puzzle grid, why must all entered numbers be primes?

88 / 100

Sub Topic: Prime puzzles (grid-based)

88. Two treasures are placed on numbers 18 and 45. What jump sizes will make Jumpy land on both treasures starting from 0?

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Sub Topic: Product of primes

89. (A) The numbers 105 and 64 are co-prime.
(R) Their prime factorizations do not share any common prime factors.

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Sub Topic: Product of primes

90. Which pair of numbers below are co-prime?

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Sub Topic: Product of primes

91. Which of the following represents the correct prime factorisation of 90?

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Sub Topic: Sum properties

92. What is the largest common factor of 20 and 28?

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Sub Topic: Sum properties

93. In a treasure hunt game, treasures are placed at positions 36 and 48. What jump sizes will land on both these positions?

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Sub Topic: Sum properties

94. (A) The number 6 is a perfect number.
(R) A perfect number is defined as a number for which the sum of all its factors equals twice the number.

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Sub Topic: Finding unique number sets

95. (A) In the set \{9, 16, 25, 43\}, 9 is special because it is a single-digit number.
(R) All other numbers in the set are two-digit numbers.

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Sub Topic: Finding unique number sets

96. In the set \{9, 16, 25, 43\}, which number does not belong because it is not a perfect square?

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Sub Topic: Finding unique number sets

97. From the given set \{3, 8, 11, 24\}, identify the number that is a prime number.

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Sub Topic: Engaging students in mathematical reasoning

98. Which of the following numbers is divisible by 8?

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Sub Topic: Engaging students in mathematical reasoning

99. (A) The number 8536 is divisible by 4.
(R) A number is divisible by 4 if the last two digits form a number that is divisible by 4.

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Sub Topic: Engaging students in mathematical reasoning

100. Which of the following numbers is a prime number?

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