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. In a treasure hunt game, treasures are placed at multiples of both 8 and 12. Which of the following could be the position of a treasure?

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

3. In the "Idli-Vada" game, at what number is 'idli-vada' said for the 5th time?

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

4. In the "Idli-Vada" game, if the two numbers chosen are co-prime, what will be the difference between the first occurrence of "vada" and the first occurrence of "idli-vada"?

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

5. Find the least common multiple (LCM) of 8, 12, and 16.

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

6. 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: Jumpy and Grumpy’s treasure jump game

7. (A) If treasures are placed on 15 and 28, Jumpy cannot land on both with any jump size greater than 1.
(R) The numbers 15 and 28 have no common factors other than 1.

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Sub Topic: Jumpy and Grumpy’s treasure jump game

8. If Jumpy chooses a jump size of 5, which treasure number(s) can he reach starting from 0?

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Sub Topic: Introduction to factors and multiples

9. Using prime factorisation, determine which of the following pairs has the first number divisible by the second?

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Sub Topic: Introduction to factors and multiples

10. Which pair of numbers are co-prime?

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Sub Topic: Games and visualizations using number grids

11. In the Idli-Vada game, if the game is played for numbers 1 to 120, how many times will 'idli-vada' be said?

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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. Which of the following numbers is a composite number?

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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. (A) The number $1$ is a prime number.
(R) A prime number has exactly two distinct factors.

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Sub Topic: Understanding prime and composite numbers

16. (A) The number 9 is a composite number.
(R) The number 9 has more than two factors.

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Sub Topic: Rectangular arrangements to visualize factors

17. A farmer wants to arrange 24 apples in different rectangular patterns. How many unique rectangular arrangements are possible for 24 apples?

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Sub Topic: Rectangular arrangements to visualize factors

18. (A) The number 9 is a composite number.
(R) A composite number has more than two factors, and 9 has factors 1, 3, and 9.

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

19. Which of the following numbers is a prime between 50 and 60?

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

20. After applying the Sieve of Eratosthenes up to 100, what is the largest gap between any two consecutive prime numbers in the list?

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Sub Topic: Composite numbers

21. A number has prime factorisation $2^3 \times 3^2 \times 5$. Which of the following statements about this number is correct?

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Sub Topic: Composite numbers

22. Which of the following is a composite number?

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Sub Topic: Perfect numbers

23. Which of the following numbers is a perfect number where the sum of its proper divisors (excluding itself) equals the number itself?

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Sub Topic: Perfect numbers

24. What is the sum of all proper divisors of the smallest perfect number?

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Sub Topic: Twin primes

25. Which of the following pairs is NOT a twin prime?

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Sub Topic: Twin primes

26. Which of the following pairs are twin primes?

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Sub Topic: Prime pairs with special properties

27. Which of the following primes $p$ satisfies that $2p + 1$ is also 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. Which of the following pairs are twin primes?

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Sub Topic: True or false reasoning about properties of primes

30. (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: Co-prime Numbers for Safekeeping Treasures

31. (A) The pair of numbers 18 and 35 is a safe pair for placing treasures because they are co-prime.
(R) Two numbers are co-prime if their greatest common divisor (GCD) is 1.

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Sub Topic: Co-prime Numbers for Safekeeping Treasures

32. (A) The pair of numbers 15 and 37 are co-prime because they have no common factor other than 1.
(R) Two numbers are co-prime if their greatest common divisor (GCD) is 1.

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

33. (A) The numbers 18 and 29 are co-prime.
(R) They have no common factor other than 1.

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

34. (A) The pair 15 and 39 is a safe pair of numbers for placing treasures.
(R) Two numbers are co-prime if they have no common factor other than 1.

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Sub Topic: Applying this concept to treasure game strategies

35. Which rule must be followed to solve the prime puzzle correctly?

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Sub Topic: Applying this concept to treasure game strategies

36. Grumpy wants to place two treasures on two different numbers such that Jumpy cannot reach both treasures with any jump size other than 1. Which of the following pairs should Grumpy choose?

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Sub Topic: Examples of co-prime pairs

37. A bank uses two numbers $m$ and $n$ as part of its security code, where $m = 17 \times 23$ and $n = 19 \times 29$. Are $m$ and $n$ co-prime? Will changing $n$ to $19 \times 23$ affect their co-primality?

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Sub Topic: Examples of co-prime pairs

38. (A) The pair (8, 15) is co-prime because their greatest common divisor (GCD) is 1.
(R) Two numbers are co-prime if they do not share any common prime factors.

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Sub Topic: Relationship between co-primes and LCM

39. In a thread art setup with $n$ pegs and a thread-gap of $k$, the thread will tie every peg if and only if:

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Sub Topic: Relationship between co-primes and LCM

40. Which of the following pairs of numbers are NOT co-prime based on their prime factorizations?

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Sub Topic: Visualizing co-primes using thread art

41. If the sum of two co-prime numbers is 23, and their difference is 1, what are these numbers?

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Sub Topic: Visualizing co-primes using thread art

42. When is the first common multiple of two numbers equal to their product?

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Sub Topic: Prime Factorisation

43. (A) The number 1 has a unique prime factorisation.
(R) A prime number is defined as a number with exactly two distinct positive divisors.

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Sub Topic: Prime Factorisation

44. A number has the prime factorisation $2^a \times 3^b \times 5^c$. If the number is divisible by both 36 and 50, what is the minimum value of $a + b + c$?

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Sub Topic: Breaking down numbers into products of prime factors

45. (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: Breaking down numbers into products of prime factors

46. If the prime factorisation of a number is $2 \times 3^2 \times 5$, what is the number?

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Sub Topic: Systematic method for factorisation

47. How many distinct prime factors does the number 30 have?

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Sub Topic: Systematic method for factorisation

48. If the prime factorisation of a number is $2 \times 3 \times 5^2$, what is the number?

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Sub Topic: Prime factorisation of products

49. Is 120 divisible by 15? Use their prime factorisations to determine the answer.

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Sub Topic: Prime factorisation of products

50. (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: Uniqueness of prime factorisation (order doesn’t matter)

51. What is the prime factorisation of 30, considering the uniqueness of prime factors?

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

52. Which of the following products represents a different prime factorisation of 180 compared to others?

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Sub Topic: Use of prime factorisation to:

53. A number $x$ has the prime factorization $2^3 \times 5 \times 7$, and another number $y$ has the prime factorization $3^2 \times 11 \times 13$. Which of the following statements is true?

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Sub Topic: Use of prime factorisation to:

54. (A) If the prime factorisations of two numbers $a$ and $b$ share a common prime factor, then $ab$ is not divisible by their least common multiple (LCM).

(R) The LCM of two numbers is the product of all unique prime factors raised to their highest powers present in either number.

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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?

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Sub Topic: Check divisibility

57. (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: Check divisibility

58. If a number $M$ is divisible by both $12$ and $15$, what is the smallest possible exponent of $2$ in its prime factorisation?

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Sub Topic: Prime factorisation of a product of two numbers

59. Determine the prime factorisation of $1000 \times 81$.

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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. Check whether 45 and 56 are co-prime using prime factorisation.

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

62. (A) The numbers 15 and 28 are co-prime.
(R) There are no common prime factors in the prime factorisations of 15 and 28.

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

63. (A) If a number $N$ is divisible by another number $M$, then the prime factorisation of $N$ must include all prime factors of $M$ with at least the same multiplicity.
(R) The divisibility rule based on prime factorisation holds because it ensures that $N$ can be expressed as a product of $M$ and another integer.

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

64. (A) The number $180$ is divisible by $15$.
(R) The prime factorisation of $15$ ($3 \times 5$) is included in the prime factorisation of $180$ ($2 \times 2 \times 3 \times 3 \times 5$).

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Sub Topic: Divisibility Tests

65. What is the smallest 4-digit number divisible by both 4 and 8?

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Sub Topic: Divisibility Tests

66. A 4-digit number has its first three digits as 576. What should be its last digit to make it divisible by both 4 and 8?

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

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

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

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

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Sub Topic: Identifying patterns using last digits

69. A six-digit number has its last three digits as $\overline{abc}$. If $\overline{abc}$ is divisible by 8 and $\overline{bc}$ is divisible by 4, what can be concluded about the original six-digit number?

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Sub Topic: Identifying patterns using last digits

70. A number when divided by 5 leaves a remainder of 3 and when divided by 10 leaves a remainder of 8. If the sum of two such numbers is considered, which of the following statements is true about the resulting sum?

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Sub Topic: Using divisibility rules to simplify calculations

71. (A) The number 3128 is divisible by both 4 and 8.

(R) A number divisible by 8 must also be divisible by 4.

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Sub Topic: Using divisibility rules to simplify calculations

72. (A) A number is divisible by 8 if the number formed by its last three digits is divisible by 8.
(R) Every number divisible by 8 must also be divisible by 4 since 8 is a multiple of 4.

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Sub Topic: Exploring palindromes and leap years through divisibility

73. Which pair of numbers can be used to confirm that 14560 is divisible by all of 2, 4, 5, 8, and 10 at once?

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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. (A) The number 980 is divisible by 10 because its units digit is 0.
(R) A number is divisible by 10 if its units digit is 0.

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Sub Topic: Exercises to find remainders and apply logic

76. What is the remainder when 4873 is divided by 5?

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Sub Topic: Fun with Numbers

77. In the set of numbers 9, 16, 25, 43, which number is special because it is NOT a perfect square?

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Sub Topic: Fun with Numbers

78. Which number in the set 5, 7, 12, 35 is special because it is the only multiple of both 3 and 4?

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Sub Topic: Fun with Numbers

79. (A) 43 is a special number among the set \{9, 16, 25, 43\} because it is the only prime number in the set.
(R) A prime number has exactly two distinct factors: 1 and itself.

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

80. Which pair of numbers is co-prime?

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

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

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

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

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Sub Topic: Puzzles involving:

83. What jump sizes will land on both 28 and 70 in the treasure hunting game?

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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. Grumpy has kept treasures on the numbers 28 and 70 in the treasure hunting game. Which jump sizes will allow Jumpy to land on both the numbers?

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Sub Topic: Prime puzzles (grid-based)

86. In the example box $5$ $7$ $12$ $35$, which number is not a prime?

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Sub Topic: Prime puzzles (grid-based)

87. (A) In a prime puzzle grid, the product of the numbers in each row must equal the number to the right of the row.
(R) All entries in the grid must be prime numbers.

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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 prime factorisation of 30 is $2 \times 3 \times 5$.
(R) Every composite number can be expressed as a product of primes, and this representation is unique up to the order of factors.

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Sub Topic: Product of primes

90. (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

91. What is the prime factorisation of 30?

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Sub Topic: Sum properties

92. (A) The number 6 is a perfect number.
(R) The sum of the factors of 6 (1, 2, 3, and 6) equals twice the number itself.

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Sub Topic: Sum properties

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

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Sub Topic: Sum properties

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

95 / 100

Sub Topic: Finding unique number sets

95. (A) In the set {9, 16, 25, 43}, the number 25 is special because it is the only multiple of 5.
(R) A number is special in a set if it has a unique property that distinguishes it from the other numbers.

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Sub Topic: Finding unique number sets

96. (A) In the set \{$5$, $7$, $12$, $35$\}, the number $12$ is special because it is the only composite number that is neither a prime nor a multiple of $5$.
(R) The number $12$ can be expressed as the sum of two prime numbers ($5 + 7$) which is not possible for any other number in the given set.

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Sub Topic: Finding unique number sets

97. 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: Engaging students in mathematical reasoning

98. (A) The numbers 18 and 35 are co-prime because they have no common factor other than 1.
(R) Two numbers are said to be co-prime if their greatest common divisor (GCD) is 1.

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Sub Topic: Engaging students in mathematical reasoning

99. If two numbers are co-prime, what is their least common multiple (LCM)?

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Sub Topic: Engaging students in mathematical reasoning

100. A $3 \times 3$ grid is filled with prime numbers such that the product of numbers in each row matches the number to its right, and the product of numbers in each column matches the number below it. The products for rows are 30, 63, and 170 from top to bottom. The products for columns are 42, 75, and 102 from left to right. What could be the missing prime number in the center cell?

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