Number System for SOF IMO Grade 5–8

Number System for SOF IMO (Class 5–8)

Complete Concept Guide + 90 Olympiad-Level Practice Questions

The Number System is the backbone of Mathematics Olympiad exams. In SOF IMO, nearly 30–40% of the paper directly or indirectly depends on number system concepts. Students who master this topic gain a strong advantage across arithmetic, algebra, and logical reasoning questions.

This complete guide explains all important number system concepts for Class 5 to Class 8, followed by 90 high-quality Olympiad questions designed strictly according to IMO standards.

What is Number System in SOF IMO?

The number system deals with:

Understanding different types of numbers

Properties and relationships between numbers

Logical application of divisibility, factors, and place value

IMO questions focus more on thinking and application rather than direct calculations.

Number System Syllabus for SOF IMO (Class 5–8)

🔹 Class 5 Focus Areas

Place value and face value

Comparison of numbers

Factors and multiples

Prime and composite numbers

Divisibility rules

LCM and HCF (basic)

🔹 Class 6 Focus Areas

Whole numbers and integers

Properties of numbers

Factors and multiples

Prime factorization

LCM and HCF

Divisibility tests

🔹 Class 7 Focus Areas

Integers (operations)

Rational numbers

Properties of operations

Exponents (basic)

Word problems on number system

🔹 Class 8 Focus Areas

Rational and irrational numbers

Squares and square roots

Cubes and cube roots

Laws of exponents

Olympiad-level number patterns

Important Number System Concepts for IMO

Prime and composite numbers

Co-prime numbers

Even and odd properties

Divisibility rules (2 to 11)

LCM and HCF applications

Remainders

Perfect squares and cubes

Number patterns and sequences

Expert Tips to Score High in Number System (IMO)

 Use factorization instead of long division

 Memorize divisibility rules clearly

 Practice remainder-based questions

 Check options using elimination

  Avoid careless calculation errors

 90 SOF IMO Number System Practice Questions (Class 5–8)

 EASY LEVEL (Class 5 Standard) – Q1 to Q30

1. Find the smallest 3-digit number divisible by 6.

2. Which of the following is a prime number: 21, 29, 35, 49?

3. How many factors does 12 have?

4. Find the LCM of 4 and 6.

5. Find the HCF of 18 and 24.

6. Which number is divisible by both 3 and 5: 30, 32, 34, 36?

7. Write the smallest prime number.

8. Find the next prime number after 13.

9. Is 1 a prime or composite number?

10. How many even numbers are there between 1 and 20?

11. Find the place value of 7 in 37,462.

12. Which is the smallest composite number?

13. Find the sum of the first five natural numbers.

14. How many multiples of 5 are there between 1 and 50?

15. Which number is divisible by 9: 234, 235, 236?

16. Find the HCF of 16 and 20.

17. Write all factors of 15.

18. Which of these is a perfect square: 16, 18, 20, 22?

19. Find the greatest 2-digit number divisible by 7.

20. Find the least number divisible by 4 and 10.

21. Which is an odd prime number?

22. Find the number of digits in 9,876.

23. Find the smallest 4-digit number.

24. Write the predecessor of 1,000.

25. Find the successor of 9,999.

26. How many prime numbers are there between 1 and 10?

27. Which number is divisible by 11: 121, 123, 125?

28. Find the LCM of 3, 4.

29. Find the HCF of 9 and 27.

30. Which is greater: 5² or 24?

 MEDIUM LEVEL (Class 6–7 Standard) – Q31 to Q60

31. Find the least number which when divided by 8 leaves remainder 3.

32. Find the smallest number divisible by 12, 15, and 20.

33. How many prime numbers are there between 20 and 50?

34. Find the HCF of 36, 48, and 60.

35. If a number is divisible by 6, is it always divisible by 3?

36. Find the value of 2³ × 2⁴.

37. Which of the following is not a perfect cube: 27, 64, 125, 216?

38. Find the smallest 5-digit number divisible by 9.

39. If LCM of two numbers is 120 and HCF is 6, find the product of the numbers.

40. Find the remainder when 37 is divided by 5.

41. How many factors does 36 have?

42. Find the greatest number that divides 42 and 70 exactly.

43. Find the smallest prime factor of 91.

44. Which is greater: 3⁴ or 4³?

45. Find the value of (–3)².

46. How many integers lie between –10 and 10?

47. Find the successor of –1.

48. Which number is divisible by 8: 256, 258, 262?

49. Find the cube root of 125.

50. Find the square root of 196.

51. If a number is divisible by 9, what about the sum of its digits?

52. Write the prime factorization of 72.

53. Find the smallest number which leaves remainder 5 when divided by 7.

54. Find the least number divisible by 5 and 7.

55. Which is the smallest composite number?

56. Find the value of 10⁰.

57. Which of the following is an integer: –5, 2/3, 0.25?

58. How many prime numbers are less than 30?

59. Find the value of 3² + 4².

60. Find the HCF of 54 and 81.

 HARD LEVEL (Class 8 + Olympiad) – Q61 to Q90

61. Find the smallest number which when divided by 6, 8, and 12 leaves remainder 1.

62. If the HCF of two numbers is 12 and their product is 1800, find their LCM.

63. Find the number of trailing zeros in 5!

64. Which is greater: 2⁵ × 2³ or 4⁴?

65. Find the smallest number which is divisible by all numbers from 1 to 10.

66. If p is a prime number, what is the smallest value of p² – 1?

67. How many perfect squares lie between 1 and 100?

68. Find the remainder when 2⁷ is divided by 3.

69. Find the smallest prime factor of 143.

70. If a number leaves remainder 2 when divided by 5, what is the remainder when it is divided by 10?

71. Find the value of (–2)³ × (–2)².

72. Which of the following is an irrational number: √2, √4, √9?

73. Find the smallest number which when divided by 9 leaves remainder 7.

74. Find the number of factors of 64.

75. Find the value of 3⁰ + 5⁰.

76. How many integers are there between –25 and 25?

77. Find the greatest 3-digit number divisible by 11.

78. Which number is both a square and a cube?

79. Find the value of √144 + ∛27.

80. If a number is divisible by 12, which of the following must divide it: 3, 4, 6?

81. Find the smallest composite number having exactly three prime factors.

82. Find the remainder when 10⁴ is divided by 9.

83. Which is greater: √81 or ∛125?

84. Find the smallest number which when divided by 4, 5, 6 leaves same remainder.

85. Find the value of 7² − 5².

86. How many prime numbers lie between 50 and 100?

87. If x is an even prime number, find x².

88. Find the smallest number divisible by 16, 20, and 24.

89. Which number has exactly two factors?

90. Find the value of (3²)³.

Olympiad Expert Advice

Number system questions in SOF IMO are designed to test concept clarity, not speed. Students should focus on understanding properties rather than memorizing shortcuts. Daily practice of mixed-level problems is the key to Olympiad success.

Stay connected with Olymp Math for complete Olympiad preparation guides, worksheets, and expert strategies for Classes 1–10.