Class 6 Knowing Our Numbers Whole Numbers and Playing with Numbers Olympiad

  

   

Knowing Our Numbers, Whole Numbers and Playing with Numbers for Class 6 Olympiad

Introduction

Numbers are everywhere — in money, time, distance, and even in games. But Olympiad math is not just about reading numbers. It’s about understanding how numbers behave, how they connect, and how we can play with them smartly.

If your child can “see” patterns in numbers, break them, and rebuild them, Olympiad questions become much easier. This chapter builds that exact power.

Knowing Our Numbers

Large numbers can look confusing, but they follow a simple system.

Example
5,43,276

This is read as:
5 lakh 43 thousand 276

Visual Understanding

Imagine numbers as groups:
Ones → small dots
Thousands → small boxes
Lakhs → big boxes

So instead of a long number, think of it as organized blocks.

Example

Write 706504 in Indian system

Answer
7,06,504

Whole Numbers

Whole numbers start from 0 and go on forever.

0, 1, 2, 3, 4, …

Properties of whole numbers:
Closure: a + b is always a whole number
Example: 5 + 3 = 8

Commutative: a + b = b + a
Example: 4 + 7 = 7 + 4

Associative: (a + b) + c = a + (b + c)

Visual Understanding

Think of whole numbers like steps on a staircase starting from 0. You can only go forward.

Playing with Numbers

This includes factors, multiples, primes, divisibility rules.

Factors

Factors divide a number exactly.

Example
Factors of 12: 1, 2, 3, 4, 6, 12

Multiples

Multiples are results of multiplication.

Example
Multiples of 5: 5, 10, 15, 20

Prime Numbers

Numbers with only 2 factors: 1 and itself

Example
2, 3, 5, 7

Divisibility Rules

2 → last digit even
3 → sum of digits divisible by 3
5 → last digit 0 or 5
9 → sum divisible by 9

Example

Check 234 divisible by 3

2 + 3 + 4 = 9 → divisible by 3

Common Mistakes

Students often:
read large numbers incorrectly
forget place values
mix factors and multiples
forget divisibility rules
skip checking steps

Short Tricks

Break numbers into parts
Use digit sum for divisibility
Remember prime numbers till 20
Use factor pairs method
Practice mental math daily

Practice Questions

Easy Level

1. Write 45678 in words

2. Place value of 7 in 67892

3. Greatest 4-digit number

4. Smallest 5-digit number

5. Successor of 999

6. Predecessor of 1000

7. 0 is a whole number or not

8. 5 + 3 = ?

9. Factors of 10

10. Multiples of 3 up to 15

11. Is 7 prime

12. Even numbers between 1 and 10

13. Write 70000 + 3000 + 20 + 5

14. Divisible by 2: 45, 48

15. Sum of digits of 123

16. Is 9 divisible by 3

17. Count digits in 45678

18. Write 1 lakh in numbers

19. Largest 3-digit number

20. Smallest whole number

21. Write 98000 + 600 + 4

22. Is 11 prime

23. Factors of 8

24. Multiples of 4

25. Divisible by 5: 27, 50

26. Write number name of 345

27. Sum of 6 + 7

28. Predecessor of 200

29. Successor of 9999

Medium Level

30. Write 507030 in Indian system

31. Place value of 5 in 356789

32. Compare: 654321 and 654123

33. Factors of 18

34. Multiples of 7 up to 50

35. Is 29 prime

36. Find LCM of 4 and 6

37. Find HCF of 8 and 12

38. Check divisibility of 123 by 3

39. Write expanded form of 45678

40. Find next multiple of 9 after 45

41. Even numbers between 20 and 30

42. Prime numbers between 10 and 20

43. Sum of digits of 987

44. Is 121 divisible by 11

45. Write 3 lakh in numbers

46. Arrange: 23456, 23465, 23546

47. Find factors of 20

48. Find multiples of 6

49. Check 100 divisible by 4

50. Find difference: 10000 – 9999

51. Write smallest 6-digit number

52. Write largest 5-digit number

53. Is 51 divisible by 3

54. Count factors of 16

Hard Level (IMO Level)

55. Find HCF of 24, 36, 60

56. Find LCM of 12 and 15

57. Largest 4-digit number divisible by 9

58. Smallest number divisible by 2, 3, 5

59. Number divisible by both 4 and 6

60. Find sum of first 10 whole numbers

61. Find prime numbers between 20–40

62. Find missing: 2, 6, 7, 21, __

63. Find remainder: 100 ÷ 9

64. Check divisibility of 999 by 9

65. Number with 3 factors

66. Find factors of 36

67. Find common multiples of 3 and 4

68. Find HCF of 15 and 25

69. Find LCM of 8 and 10

70. Write greatest 6-digit number

71. Write smallest 7-digit number

72. Find next prime after 31

73. Find sum of factors of 10

74. Find product of first 5 whole numbers

75. Number divisible by 2 and 3

76. Check 1001 divisible by 7

77. Find difference: 100000 – 99999

78. Find sum of digits of 9999

79. Find smallest multiple of 8 greater than 50

Answer Key with Explanations

Easy

1. Forty five thousand six hundred seventy eight

2. 7000

3. 9999

4. 10000

5. 1000

6. 999

7. Yes

8. 8

9. 1, 2, 5, 10

10. 3, 6, 9, 12, 15

11. Yes

12. 2, 4, 6, 8, 10

13. 73025

14. 48

15. 6

16. Yes

17. 5

18. 100000

19. 999

20. 0

21. 98604

22. Yes

23. 1, 2, 4, 8

24. 4, 8, 12

25. 50

26. Three hundred forty five

27. 13

28. 199

29. 10000

Medium

30. 5,07,030

31. 500000

32. 654321

33. 1, 2, 3, 6, 9, 18

34. 7, 14, 21, 28, 35, 42, 49

35. Yes

36. 12

37. 4

38. Yes

39. 40000 + 5000 + 600 + 70 + 8

40. 54

41. 22, 24, 26, 28

42. 11, 13, 17, 19

43. 24

44. Yes

45. 300000

46. 23456, 23465, 23546

47. 1, 2, 4, 5, 10, 20

48. 6, 12, 18

49. Yes

50. 1

51. 100000

52. 99999

53. Yes

54. 5

Hard

55. 12

56. 60

57. 9999

58. 30

59. 12

60. 55

61. 23, 29, 31, 37

62. 22

63. 1

64. Yes

65. 4

66. 1, 2, 3, 4, 6, 9, 12, 18, 36

67. 12, 24

68. 5

69. 40

70. 999999

71. 1000000

72. 37

73. 18

74. 0

75. multiples of 6

76. Yes

77. 1

78. 36

79. 56

Olympiad success in numbers is all about practice and smart thinking.

Encourage your child to break numbers, explore patterns, and challenge themselves daily. That is how number mastery is built.