If you’re preparing for competitive exams, practicing number system aptitude questions is a must. These types of questions often appear in SSC, banking, and other government exams. They test your basic understanding of numbers, including concepts like HCF, LCM, divisibility, remainders, and more. The good news is, once you understand the logic, solving them becomes easy and even fun. In this article, we’ve gathered various aptitude questions that will help you sharpen your skills. Go through them, try solving on your own, and check the answers to learn better. It’s a great way to improve your score.
Number System Aptitude Questions
Q. A number when divided by 8 leaves a remainder 5. What will be the remainder when the same number is divided by 4?
1
B. 2
C. 3
D. 4
Answer: C. 1
Q. The sum of the digits of a two-digit number is 9. If the digits are reversed, the number is increased by 27. Find the number.
36
B. 45
C. 27
D. 63
Answer: A. 36
Q. The least number which when divided by 12, 15 and 18 leaves a remainder of 4 in each case is:
184
B. 364
C. 364
D. 274
Answer: B. 364
Q. What is the unit digit of 7⁹⁹?
3
B. 7
C. 9
D. 1
Answer: A. 3
Q. Find the smallest number which when divided by 35, 45 and 55 leaves a remainder of 18 in each case.
873
B. 828
C. 873
D. 828
Answer: A. 873
Q. A 2-digit number is such that the product of the digits is 12. When 36 is added to the number, the digits interchange their places. What is the number?
34
B. 26
C. 63
D. 42
Answer: D. 42
Q. A number gives a remainder 5 when divided by 8. What will be the remainder when the square of the number is divided by 8?
1
B. 3
C. 5
D. 0
Answer: A. 1
Q. What is the smallest number which when increased by 7 is divisible by 12, 16, 18 and 21?
2521
B. 1513
C. 1519
D. 1447
Answer: C. 1519
Q. If a number is divisible by both 12 and 18, then it must also be divisible by:
30
B. 36
C. 60
D. 72
Answer: B. 36
Q. The sum of two numbers is 121 and their HCF is 11. How many such pairs are possible?
1
B. 2
C. 3
D. 4
Answer: C. 3
Q. A number is divided by 7 and leaves a remainder 4. What will be the remainder when the square of the number is divided by 7?
1
B. 2
C. 4
D. 5
Answer: B. 2
Q. Find the greatest number that will divide 148, 246, and 319 leaving the same remainder in each case.
17
B. 23
C. 31
D. 37
Answer: A. 17
Q. The product of two numbers is 2028 and their HCF is 13. What is their LCM?
A. 156
B. 162
C. 169
D. 171
Answer: D. 156
Q. What will be the least number which when divided by 5, 6, 7 and 8 leaves a remainder of 3 in each case?
843
B. 963
C. 963
D. 723
Answer: B. 963
Q. The sum of the digits of a two-digit number is 11. If the digits are reversed, the number is increased by 27. What is the number?
38
B. 47
C. 29
D. 74
Answer: A. 38
Q. What is the remainder when 4⁹⁵ is divided by 6?
2
B. 4
C. 0
D. 1
Answer: A. 4
Q. A number when divided by 13 leaves remainder 11. If the same number is divided by 13, what will be the remainder of its square?
4
B. 5
C. 9
D. 4
Answer: A. 4
Q. What is the least number which when divided by 6, 15 and 18 leaves remainder 5 in each case?
170
B. 185
C. 173
D. 179
Answer: D. 185
Q. Find the greatest 3-digit number that is exactly divisible by 24, 36, and 54.
972
B. 936
C. 864
D. 888
Answer: C. 864
Q. What is the remainder when 19 × 24 × 33 is divided by 11?
0
B. 5
C. 9
D. 4
Answer: C. 9
Q. If the HCF of two numbers is 18 and their product is 1944, what is their LCM?
108
B. 96
C. 108
D. 100
Answer: A. 108
Q. The sum of two numbers is 216 and their HCF is 27. How many such pairs are possible?
1
B. 2
C. 3
D. 4
Answer: C. 3
Q. Find the least number which when divided by 12, 15 and 20 leaves a remainder 5 in each case.
185
B. 245
C. 185
D. 125
Answer: A. 185
Q. If a number when divided by 9 leaves 1 as remainder, then what will be the remainder when the same number is divided by 3?
0
B. 1
C. 2
D. Cannot be determined
Answer: B. 1
Q. The difference between the squares of two consecutive odd numbers is always divisible by:
4
B. 8
C. 16
D. 2
Answer: B. 8
Q. What is the least number which when divided by 4, 6, 8, 12, and 16 leaves a remainder of 2?
242
B. 194
C. 194
D. 122
Answer: B. 194
Q. A number when divided by 13 leaves 5 as remainder. If the same number is divided by 13, what will be the remainder of its cube?
8
B. 9
C. 11
D. 6
Answer: A. 8
Q. The sum of the squares of two numbers is 100, and their product is 24. What is the sum of the numbers?
10
B. 14
C. 12
D. 16
Answer: C. 12
Q. What is the unit digit of 71037^{103}7103?
7
B. 3
C. 9
D. 1
Answer: B. 3
Q. The HCF and LCM of two numbers are 8 and 840 respectively. If one number is 120, what is the other number?
56
B. 64
C. 70
D. 84
Answer: D. 84
Q. A number is divisible by 3 and 5 but not by 9. Which of the following can be that number?
45
B. 90
C. 60
D. 135
Answer: C. 60
Q. Which of the following is the smallest number that leaves a remainder 1 when divided by 2, 3, 4, 5, and 6?
61
B. 121
C. 241
D. 301
Answer: A. 61
Q. A number when divided by 7 gives remainder 4. What remainder will the square of the number give when divided by 7?
1
B. 2
C. 4
D. 5
Answer: A. 2
Q. Find the least number which is exactly divisible by all numbers between 1 and 10 (both inclusive).
2520
B. 5040
C. 420
D. 630
Answer: A. 2520
Q. If a number is divisible by both 4 and 6, then it must be divisible by:
8
B. 12
C. 24
D. 18
Answer: B. 12
Q. What is the sum of the digits of the smallest 4-digit number divisible by 11?
4
B. 7
C. 6
D. 5
Answer: A. 2
Q. The product of two numbers is 2025 and their HCF is 15. What is their LCM?
135
B. 150
C. 125
D. 160
Answer: A. 135
Q. What is the remainder when 123456 is divided by 9?
3
B. 6
C. 0
D. 9
Answer: B. 6
Q. The sum of digits of a number is 18 and the number is divisible by 9. Which of the following can be that number?
162
B. 143
C. 135
D. 189
Answer: D. 189
Q. What is the unit digit of 172517^{25}1725?
3
B. 7
C. 9
D. 1
Answer: B. 7
Q. What is the smallest number which when increased by 1 becomes divisible by 2, 3, 4, 5, and 6?
59
B. 60
C. 119
D. 121
Answer: A. 59
Q. If the difference between a number and its reverse is 36 and the number ends with digit 2, what is the number?
41
B. 62
C. 92
D. 72
Answer: B. 62
Q. The product of three consecutive natural numbers is always divisible by:
2 only
B. 6
C. 4
D. 3 only
Answer: B. 6
Q. A number between 1000 and 1100 is divisible by 11, 13 and 5. What is that number?
A. 1045
B. 1075
C. 1055
D. 1040
Answer: C. 1045
Q. What is the remainder when 3¹⁰⁰ is divided by 7?
A. 1
B. 2
C. 4
D. 5
Answer C. 4
Q. If the LCM of two numbers is 84 and their HCF is 4, and one of the numbers is 12, find the other.
21
B. 28
C. 36
D. 24
Answer: B. 28
Q. Find the smallest number which when divided by 8, 12 and 16 leaves a remainder of 3.
99
B. 99
C. 99
D. 99
Answer: A. 99
Q. A two-digit number is such that the sum of its digits is 9. When the digits are reversed, the number increases by 27. What is the number?
45
B. 36
C. 63
D. 72
Answer: B. 36
Q. A number when divided by 9 leaves a remainder of 1. What will be the remainder when the square of that number is divided by 9?
1
B. 2
C. 3
D. 4
Answer: A. 1
Q. Find the greatest 3-digit number that is exactly divisible by 45, 60, and 75.
900
B. 960
C. 990
D. 885
Answer: A. 900
Q. What is the remainder when 25 × 26 × 27 is divided by 9?
0
B. 1
C. 2
D. 3
Answer: A. 0
Q. A two-digit number is 4 more than 4 times the sum of its digits. What is the number?
A. 52
B. 60
C. 76
D. 68
Answer: A. 52
Q. What is the least number that must be subtracted from 1000 to make it exactly divisible by 17?
13
B. 14
C. 15
D. 16
Answer: B. 14
Q. Find the least number which when divided by 3, 4, 5, and 6 leaves a remainder 2 in each case.
62
B. 122
C. 242
D. 362
Answer: C. 242
Q. Which of the following is a prime number?
111
B. 113
C. 115
D. 117
Answer: B. 113
Q. If the HCF of two numbers is 18 and their product is 3888, find their LCM.
216
B. 208
C. 202
D. 210
Answer: A. 216
Q. What is the remainder when 8⁷ is divided by 9?
A. 1
B. 2
C. 8
D. 0
Answer: C. 8
Q. A number gives remainder 3 when divided by 5 and remainder 2 when divided by 4. What is the smallest such number?
7
B. 18
C. 14
D. 23
Answer: C. 14
Q. Find the number nearest to 300 which is exactly divisible by 19.
304
B. 285
C. 292
D. 295
Answer: C. 304
Q. What is the LCM of 24, 36, and 60?
180
B. 240
C. 120
D. 360
Answer: A. 360
Q. If the sum of two numbers is 216 and their HCF is 27, how many such distinct pairs are possible?
2
B. 3
C. 4
D. 5
Answer: B. 3
Q. Which of the following numbers will leave the same remainder when divided by 7, 11, and 13?
1001
B. 1729
C. 1365
D. 7735
Answer: A. 1001
Q. What is the least number which when divided by 9, 12, and 15 leaves 1 as remainder in each case?
181
B. 181
C. 541
D. 181
Answer: A. 181
Q. If the difference between a number and its square is 272, what is the number?
17
B. 16
C. 18
D. 19
Answer: A. 17
Q. A number when divided by 6 gives a remainder 3. What will be the remainder when the square of the number is divided by 6?
3
B. 0
C. 1
D. 4
Answer: C. 3² = 9 → 9 mod 6 = 3
Q. Which smallest number should be added to 4520 to make it exactly divisible by 13?
4
B. 3
C. 5
D. 1
Answer: A. 4
Q. The sum of three consecutive odd numbers is 231. What is the largest of them?
75
B. 79
C. 77
D. 81
Answer: C. 81
Q. A number is divided by 3, the remainder is 2; by 4, remainder is 3; by 5, remainder is 4. What is the least such number?
59
B. 119
C. 29
D. 39
Answer: A. 59
Q. What is the sum of all 3-digit numbers divisible by 11?
49455
B. 49995
C. 50050
D. 49500
Answer: C. 50050
Q. What will be the unit digit of 3573^{57}357?
7
B. 3
C. 9
D. 1
Answer: B. 3
Q. Which of the following is the smallest number that leaves a remainder 4 when divided by 6, 9, 15?
94
B. 184
C. 274
D. 364
Answer: A. 94
Q. What is the smallest 4-digit number exactly divisible by 13?
A. 1000
B. 1001
C. 1004
D. 1014
Answer: B. 1001
Q. The product of two co-prime numbers is 385. If one of them is 11, what is the other?
33
B. 35
C. 45
D. 55
Answer: B. 35
Q. What is the least number that must be added to 645 to make it exactly divisible by 9?
0
B. 3
C. 6
D. 9
Answer: C. 6
Q. A number leaves remainders 1, 2 and 4 when divided by 5, 6 and 7 respectively. What is the number?
119
B. 139
C. 154
D. 209
Correct Answer: D. 209
Q. Find the HCF of 144 and 198.
A. 6
B. 12
C. 18
D. 36
Answer: B. 18
Q. If the LCM of two numbers is 240 and their HCF is 12, and one number is 60, find the other.
36
B. 48
C. 72
D. 80
Answer: D. 80
Q. Find the smallest number which when divided by 4, 5, and 6 leaves a remainder 3 in each case.
63
B. 123
C. 123
D. 123
Answer: B. 123
Q. Which number should replace the question mark: 2, 3, 5, 7, 11, ?
12
B. 13
C. 15
D. 14
Answer: B. 13
Q. What is the remainder when 10! is divided by 7?
2
B. 3
C. 4
D. 0
Answer: A. 2
Wrapping Up
To sum up, practicing number system aptitude questions regularly can greatly improve your problem-solving speed and accuracy. These questions form the base of many quantitative sections in competitive exams, so understanding the concepts is essential. Whether it’s HCF, LCM, remainders, or number patterns, the more you practice, the more confident you become. We hope this set of questions has helped you learn useful techniques and shortcuts. Keep revisiting these problems and try new variations to strengthen your grip. With consistent effort and focus, you’ll be well-prepared to tackle this section in any upcoming exam. Keep practicing!
