Number System is one of the most important topics in quantitative aptitude and mathematics for competitive examinations. Questions from this topic are frequently asked in SSC, Railway, Banking, Defence, Police and other government and entrance exams.
This practice set contains 100 Number System MCQs with answers and explanations. It covers important concepts such as natural numbers, whole numbers, integers, prime and composite numbers, factors, multiples, HCF, LCM, divisibility rules, remainders, unit digits, fractions, perfect squares and cubes.
Try to solve each question yourself before clicking on View Answer. Regular practice will help improve your calculation speed, accuracy and understanding of important number system concepts.
Q1. Which of the following is a prime number?
A. 21
B. 29
C. 39
D. 51
View Answer
29 has only two factors, 1 and 29. Therefore, it is a prime number.
Q2. Which of the following is an irrational number?
A. 3/5
B. 0.25
C. √2
D. 7/8
View Answer
√2 cannot be expressed as a ratio of two integers, so it is irrational.
Q3. What is the smallest prime number?
A. 0
B. 1
C. 2
D. 3
View Answer
2 is the smallest prime number and the only even prime number.
Q4. What is the smallest natural number?
A. 0
B. 1
C. 2
D. −1
View Answer
Natural numbers are commonly taken as 1, 2, 3, 4, … .
Q5. What is the smallest whole number?
A. −1
B. 0
C. 1
D. 2
View Answer
Whole numbers are 0, 1, 2, 3, … .
Q6. Which number is neither prime nor composite?
A. 0
B. 1
C. 2
D. 3
View Answer
The number 1 has only one positive factor, so it is neither prime nor composite.
Q7. What is the greatest two-digit prime number?
A. 89
B. 91
C. 97
D. 99
View Answer
97 is prime and is the greatest prime number below 100.
Q8. How many prime numbers are there between 1 and 10?
A. 3
B. 4
C. 5
D. 6
View Answer
The prime numbers are 2, 3, 5 and 7.
Q9. Which of the following is a composite number?
A. 17
B. 19
C. 23
D. 27
View Answer
27 has factors other than 1 and itself, such as 3 and 9.
Q10. What is the only even prime number?
A. 0
B. 1
C. 2
D. 4
View Answer
2 is divisible only by 1 and 2, making it the only even prime number.
Q11. What is the HCF of 18 and 24?
A. 3
B. 6
C. 9
D. 12
View Answer
The greatest common factor of 18 and 24 is 6.
Q12. What is the LCM of 12 and 18?
A. 24
B. 30
C. 36
D. 48
View Answer
36 is the smallest number divisible by both 12 and 18.
Q13. What is the HCF of 36 and 48?
A. 6
B. 8
C. 12
D. 16
View Answer
36 = 12 × 3 and 48 = 12 × 4. Hence, HCF = 12.
Q14. What is the LCM of 8 and 12?
A. 16
B. 20
C. 24
D. 32
View Answer
24 is the smallest number divisible by both 8 and 12.
Q15. What is the HCF of 45 and 60?
A. 5
B. 10
C. 15
D. 20
View Answer
The greatest common factor of 45 and 60 is 15.
Q16. What is the LCM of 15 and 20?
A. 30
B. 45
C. 60
D. 75
View Answer
60 is the smallest number divisible by both 15 and 20.
Q17. If the HCF of two numbers is 6 and their LCM is 180, and one number is 30, what is the other number?
A. 24
B. 30
C. 36
D. 42
View Answer
Product of two numbers = HCF × LCM = 6 × 180 = 1080.
Other number = 1080 ÷ 30 = 36.
Q18. What is the HCF of 72 and 90?
A. 9
B. 12
C. 18
D. 24
View Answer
The greatest number dividing both 72 and 90 is 18.
Q19. What is the LCM of 9, 12 and 15?
A. 90
B. 120
C. 150
D. 180
View Answer
LCM(9, 12, 15) = 180.
Q20. What is the HCF of 24, 36 and 60?
A. 6
B. 8
C. 12
D. 18
View Answer
12 is the greatest number that divides all three numbers.
Q21. What is the remainder when 25 is divided by 4?
A. 0
B. 1
C. 2
D. 3
View Answer
25 = 4 × 6 + 1.
Q22. What is the remainder when 47 is divided by 5?
A. 1
B. 2
C. 3
D. 4
View Answer
47 = 5 × 9 + 2.
Q23. What is the remainder when 123 is divided by 10?
A. 1
B. 2
C. 3
D. 4
View Answer
The remainder is the last digit when a number is divided by 10. Therefore, the remainder is 3.
Q24. What is the remainder when 256 is divided by 7?
A. 2
B. 3
C. 4
D. 5
View Answer
256 = 7 × 36 + 4.
Q25. What is the remainder when 999 is divided by 9?
A. 0
B. 1
C. 3
D. 6
View Answer
999 is exactly divisible by 9 because 9 × 111 = 999.
Q26. What is the remainder when 1001 is divided by 10?
A. 0
B. 1
C. 2
D. 9
View Answer
1001 = 10 × 100 + 1.
Q27. What is the remainder when 85 is divided by 6?
A. 0
B. 1
C. 2
D. 3
View Answer
85 = 6 × 14 + 1.
Q28. What is the remainder when 157 is divided by 12?
A. 0
B. 1
C. 5
D. 7
View Answer
157 = 12 × 13 + 1.
Q29. What is the remainder when 234 is divided by 11?
A. 1
B. 2
C. 3
D. 4
View Answer
234 = 11 × 21 + 3.
Q30. What is the remainder when 500 is divided by 9?
A. 4
B. 5
C. 6
D. 7
View Answer
500 = 9 × 55 + 5.
Q31. Which of the following numbers is divisible by 3?
A. 124
B. 235
C. 417
D. 521
View Answer
4 + 1 + 7 = 12, which is divisible by 3.
Q32. Which of the following numbers is divisible by 9?
A. 234
B. 315
C. 425
D. 512
View Answer
3 + 1 + 5 = 9, so 315 is divisible by 9.
Q33. Which of the following numbers is divisible by 11?
A. 121
B. 125
C. 135
D. 145
View Answer
121 = 11 × 11.
Q34. Which of the following numbers is divisible by 4?
A. 126
B. 138
C. 224
D. 234
View Answer
The last two digits are 24, which is divisible by 4.
Q35. Which of the following numbers is divisible by 8?
A. 216
B. 226
C. 236
D. 246
View Answer
216 ÷ 8 = 27.
Q36. Which of the following numbers is divisible by 6?
A. 124
B. 132
C. 145
D. 155
View Answer
132 is divisible by both 2 and 3, so it is divisible by 6.
Q37. Which of the following numbers is divisible by 12?
A. 144
B. 154
C. 164
D. 174
View Answer
144 is divisible by both 3 and 4, so it is divisible by 12.
Q38. Which of the following numbers is divisible by 5?
A. 234
B. 345
C. 378
D. 421
View Answer
A number divisible by 5 ends in 0 or 5.
Q39. Which of the following numbers is divisible by 10?
A. 120
B. 125
C. 135
D. 145
View Answer
A number divisible by 10 must end in 0.
Q40. Which of the following numbers is divisible by both 3 and 5?
A. 125
B. 135
C. 145
D. 155
View Answer
135 is divisible by 3 and ends in 5, so it is divisible by 5 as well.
Q41. What is the unit digit of 7²?
A. 7
B. 8
C. 9
D. 6
View Answer
7² = 49. Therefore, the unit digit is 9.
Q42. What is the unit digit of 13²?
A. 3
B. 6
C. 9
D. 2
View Answer
13² = 169. Therefore, the unit digit is 9.
Q43. What is the unit digit of 24 × 37?
A. 8
B. 6
C. 4
D. 2
View Answer
The unit digits are 4 and 7. Since 4 × 7 = 28, the unit digit is 8.
Q44. What is the unit digit of 17³?
A. 1
B. 3
C. 7
D. 9
View Answer
17³ = 4913. Therefore, the unit digit is 3.
Q45. What is the unit digit of 9⁵?
A. 1
B. 3
C. 7
D. 9
View Answer
Powers of 9 alternate between unit digits 9 and 1. An odd power has unit digit 9.
Q46. What is the unit digit of 6⁷?
A. 2
B. 4
C. 6
D. 8
View Answer
Every positive integral power of 6 ends in 6.
Q47. What is the unit digit of 23 × 24 × 25?
A. 0
B. 2
C. 4
D. 6
View Answer
The product contains factors 24 and 25. Since 24 × 25 = 600, the product ends in 0.
Q48. What is the unit digit of 3⁴?
A. 1
B. 3
C. 7
D. 9
View Answer
3⁴ = 81. Therefore, the unit digit is 1.
Q49. What is the unit digit of 8³?
A. 2
B. 4
C. 6
D. 8
View Answer
8³ = 512. Therefore, the unit digit is 2.
Q50. What is the unit digit of 12⁵?
A. 2
B. 4
C. 6
D. 8
View Answer
The unit digit follows the cycle 2, 4, 8, 6. The fifth power therefore ends in 2.
Q51. How many factors does 12 have?
A. 4
B. 5
C. 6
D. 8
View Answer
The factors of 12 are 1, 2, 3, 4, 6 and 12.
Q52. How many factors does 24 have?
A. 6
B. 8
C. 10
D. 12
View Answer
24 = 2³ × 3. Number of factors = (3 + 1)(1 + 1) = 8.
Q53. How many factors does 36 have?
A. 6
B. 8
C. 9
D. 10
View Answer
36 = 2² × 3². Number of factors = (2 + 1)(2 + 1) = 9.
Q54. How many factors does 48 have?
A. 8
B. 9
C. 10
D. 12
View Answer
48 = 2⁴ × 3. Number of factors = (4 + 1)(1 + 1) = 10.
Q55. How many factors does 100 have?
A. 6
B. 8
C. 9
D. 10
View Answer
100 = 2² × 5². Number of factors = (2 + 1)(2 + 1) = 9.
Q56. How many positive factors does 72 have?
A. 10
B. 12
C. 14
D. 16
View Answer
72 = 2³ × 3². Number of factors = (3 + 1)(2 + 1) = 12.
Q57. Which of the following is a perfect square?
A. 72
B. 81
C. 90
D. 99
View Answer
81 = 9², so it is a perfect square.
Q58. Which of the following is a perfect cube?
A. 64
B. 72
C. 81
D. 100
View Answer
64 = 4³, so it is a perfect cube.
Q59. What is the smallest perfect square greater than 50?
A. 54
B. 56
C. 64
D. 72
View Answer
8² = 64, and 64 is the first perfect square greater than 50.
Q60. What is the smallest perfect cube greater than 100?
A. 108
B. 121
C. 125
D. 144
View Answer
5³ = 125, which is the smallest perfect cube greater than 100.
Q61. What is the sum of the first 10 natural numbers?
A. 45
B. 50
C. 55
D. 60
View Answer
Sum = n(n + 1)/2 = 10 × 11/2 = 55.
Q62. What is the sum of the first 20 natural numbers?
A. 200
B. 210
C. 220
D. 230
View Answer
Sum = 20 × 21/2 = 210.
Q63. What is the sum of the first 15 odd natural numbers?
A. 225
B. 240
C. 250
D. 275
View Answer
The sum of the first n odd numbers is n². Therefore, 15² = 225.
Q64. What is the sum of the first 10 even natural numbers?
A. 100
B. 110
C. 120
D. 130
View Answer
The first 10 even numbers are 2, 4, …, 20. Their sum is 110.
Q65. What is the sum of the first 25 natural numbers?
A. 300
B. 315
C. 325
D. 350
View Answer
25 × 26/2 = 325.
Q66. What is the difference between the largest two-digit number and the smallest two-digit number?
A. 88
B. 89
C. 90
D. 91
View Answer
99 − 10 = 89.
Q67. What is the smallest three-digit number?
A. 99
B. 100
C. 101
D. 111
View Answer
The smallest three-digit number is 100.
Q68. What is the largest three-digit number?
A. 999
B. 1000
C. 998
D. 990
View Answer
999 is the largest three-digit number.
Q69. What is the smallest four-digit number?
A. 999
B. 1000
C. 1001
D. 1111
View Answer
The smallest four-digit number is 1000.
Q70. How many three-digit natural numbers are there?
A. 899
B. 900
C. 901
D. 999
View Answer
Three-digit numbers range from 100 to 999. Therefore, the count is 999 − 100 + 1 = 900.
Q71. What is the greatest number that divides 43 and 91 leaving the same remainder?
A. 12
B. 16
C. 24
D. 48
View Answer
If the same remainder is left, the required number must divide the difference between the numbers.
91 − 43 = 48.
Therefore, the greatest possible divisor is 48.
Q72. What is the greatest number that divides 65 and 89 leaving the same remainder?
A. 12
B. 18
C. 24
D. 30
View Answer
89 − 65 = 24. Therefore, the greatest number that can divide both while leaving the same remainder is 24.
Q73. What is the least number that should be added to 58 to make it divisible by 7?
A. 3
B. 5
C. 6
D. 7
View Answer
58 leaves remainder 2 when divided by 7. Therefore, 5 should be added to get 63.
Q74. What is the least number that should be subtracted from 83 to make it divisible by 9?
A. 1
B. 2
C. 3
D. 4
View Answer
83 leaves remainder 2 when divided by 9. Therefore, subtracting 2 gives 81.
Q75. What is the least number that should be added to 125 to make it divisible by 8?
A. 1
B. 2
C. 3
D. 4
View Answer
125 leaves remainder 5 when divided by 8. Therefore, 3 should be added to get 128.
Q76. What is the least number that should be subtracted from 150 to make it divisible by 11?
A. 4
B. 5
C. 6
D. 7
View Answer
150 = 11 × 13 + 7. Therefore, 7 should be subtracted.
Q77. What is the least number that should be added to 99 to make it a perfect square?
A. 20
B. 21
C. 22
D. 24
View Answer
The next perfect square after 99 is 121 = 11².
121 − 99 = 22.
Q78. What is the least number that should be added to 80 to make it a perfect square?
A. 1
B. 4
C. 9
D. 16
View Answer
81 = 9², so 1 should be added to 80.
Q79. What is the least number that should be subtracted from 150 to make it a perfect square?
A. 4
B. 5
C. 6
D. 7
View Answer
144 = 12². Therefore, 150 − 144 = 6.
Q80. What is the least number that should be multiplied by 18 to make it a perfect square?
A. 2
B. 3
C. 6
D. 8
View Answer
18 = 2 × 3². Multiplying by 2 gives 36 = 6².
Q81. Which of the following is a rational number?
A. √2
B. √3
C. π
D. 7/11
View Answer
A rational number can be expressed as p/q, where p and q are integers and q is not zero.
Q82. Which of the following is an integer?
A. 3/4
B. −7
C. 2.5
D. √5
View Answer
Integers include negative whole numbers, zero and positive whole numbers.
Q83. Which of the following is not an integer?
A. −5
B. 0
C. 7
D. 2.5
View Answer
2.5 is a decimal number and is not an integer.
Q84. Which of the following is an irrational number?
A. √9
B. √16
C. √25
D. √7
View Answer
√7 cannot be expressed as a ratio of two integers, so it is irrational.
Q85. Which fraction has a terminating decimal expansion?
A. 1/3
B. 1/6
C. 3/8
D. 2/7
View Answer
3/8 = 0.375, which is a terminating decimal.
Q86. What is 0.125 expressed as a fraction in simplest form?
A. 1/4
B. 1/8
C. 1/10
D. 1/12
View Answer
0.125 = 125/1000 = 1/8.
Q87. What is 0.75 expressed as a fraction in simplest form?
A. 1/2
B. 2/3
C. 3/4
D. 4/5
View Answer
0.75 = 75/100 = 3/4.
Q88. What is 2.5 expressed as a fraction in simplest form?
A. 3/2
B. 5/2
C. 7/2
D. 9/2
View Answer
2.5 = 25/10 = 5/2.
Q89. Which fraction is equivalent to 3/5?
A. 6/15
B. 9/15
C. 12/25
D. 15/30
View Answer
3/5 × 3/3 = 9/15.
Q90. Which fraction is the largest?
A. 2/3
B. 3/5
C. 5/8
D. 7/12
View Answer
2/3 ≈ 0.667, which is greater than 3/5 = 0.6, 5/8 = 0.625 and 7/12 ≈ 0.583.
Q91. What is the smallest number divisible by 2, 3 and 5?
A. 15
B. 20
C. 30
D. 60
View Answer
LCM of 2, 3 and 5 = 30.
Q92. What is the smallest number divisible by 4, 6 and 8?
A. 12
B. 24
C. 36
D. 48
View Answer
LCM of 4, 6 and 8 = 24.
Q93. What is the smallest number divisible by 5, 10 and 15?
A. 15
B. 20
C. 25
D. 30
View Answer
LCM of 5, 10 and 15 = 30.
Q94. What is the smallest number divisible by 6, 8 and 12?
A. 12
B. 18
C. 24
D. 36
View Answer
LCM of 6, 8 and 12 = 24.
Q95. If a number is divisible by both 4 and 6, it must be divisible by:
A. 8
B. 10
C. 12
D. 24
View Answer
LCM of 4 and 6 is 12. Therefore, every number divisible by both is divisible by 12.
Q96. What is the smallest number which, when divided by 6, 8 and 12, leaves remainder 1 in each case?
A. 13
B. 25
C. 49
D. 73
View Answer
LCM of 6, 8 and 12 = 24.
Therefore, the required number is 24 + 1 = 25.
Q97. What is the greatest two-digit number divisible by 7?
A. 91
B. 98
C. 84
D. 77
View Answer
98 = 7 × 14 and is the greatest two-digit multiple of 7.
Q98. What is the smallest three-digit number divisible by 13?
A. 104
B. 108
C. 117
D. 130
View Answer
13 × 8 = 104, and it is the first three-digit multiple of 13.
Q99. What is the greatest three-digit number divisible by 8?
A. 984
B. 992
C. 996
D. 998
View Answer
992 ÷ 8 = 124. The next multiple is 1000, which has four digits.
Q100. What is the smallest number that should be added to 456 to make it divisible by 9?
A. 2
B. 3
C. 4
D. 5
View Answer
4 + 5 + 6 = 15. The next multiple of 9 is 18, so 3 should be added. Thus, 456 + 3 = 459.
These 100 Number System Questions with Answers provide comprehensive practice for students preparing for SSC, Railway, Banking, Defence, Police and other competitive examinations. The questions cover important concepts including prime and composite numbers, HCF, LCM, divisibility, remainders, factors, unit digits, fractions and perfect squares and cubes.
For better results, try to solve every question yourself before opening the View Answer section. Understanding the underlying concepts and practising regularly can significantly improve your calculation speed and accuracy.
Keep practising Number System questions along with other quantitative aptitude topics to build a strong mathematical foundation and improve your performance in competitive exams.
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