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Number Theory Questions for IPMAT 2027 Preparation [Tips & Tricks]
May 19, 2026
Overview: Master number theory questions for the IPMAT 2027 exam with our comprehensive guide. Learn key topics like divisibility, prime numbers, and more, and practice with sample questions and papers from previous years in this blog.
Number theory is the field of mathematics associated with studying the properties and identities of integers.
Most of you might feel that this topic is vast and challenging. However, you can score well on this topic if you understand the concepts.
Are you an aspirant for the IPM but don't know how to solve number theory questions? Well, you are in the right place!
This post takes you through the sample Number Theory Questions for IPMAT, previous year's questions, and more.
So, what are you waiting for? Practice these number theory questions for IPMAT and enhance your preparation for the upcoming IPMAT 2027 exam.
Table of Contents
Important Topics under Number Theory
Before tackling the number theory questions for IPMAT 2027, review the syllabus.
There are numerous topics within the field of number theory.
However, the following are some of the important topics under the syllabus for IPMAT.
- Divisibility
- Fractions
- LCM and HCM
- Prime Numbers
- Modular arithmetic
- Arithmetic functions
- Analytical number theory
- Algebraic number theory
- Quadratic Forms
- L-functions
Sample Number Theory Questions for IPMAT 2027
Practice is the key to performing well in the IPMAT Indore exam.
Ensure that your basics are straightforward and have a good grip.
You can pen down the topics in which you are weak and strong separately.
This can help you decide which topic you need to focus more on.
You are advised to practice at least 1-2 previous year question papers for IPMAT every week, as this will help you to know the difficulty level and the type of number theory questions for the IPMAT exam.
Q) A number N=0.abcabcabc....where a,b,c are not simultaneously 0. Which of the following numbers, N, should be multiplied to get an integer product?
- a) 99
- b) 09
- c) 3996
- d) None of the above
Q) The total number of positive integers 'n' is 10 to 70, such that the product is (n-1). (n-2)......3.2.1 is not divisible by 'n' is
- a) 14
- b) 15
- c) 16
- d) 17
Q) Let E be the set of even integers 'a' from 125 to 275 where 'a' is divisible by 9 but not by 11. How many elements does 'E' contain?
- a) 12
- b) 11
- c) 8
- d) 9
Q) If 'Z' is the LCM of the first 25 natural numbers, then find the LCM of the first 30 natural numbers.
- a) 111 Z
- b) 21X22X23X24X25 Z
- c) 87 Z
- d) 123 Z
Q) A number, when divided by 4, 5, and 7, successively leaves the remainder 2, 3, and 4, respectively. Find the remainder when the same number is divided by 70.
- a) 20
- b) 64
- c) 24
- d) 35
Q) A certain number K has 8 factors. Which among the following cannot be the possible number of factors of K^3?
- a) 22
- b) 27
- c) 40
- d) 64
Q) 48 students have to be seated so each row has the same number of students as the others. If at least 3 students are to be seated per row and at least 2 rows have to be there, how many arrangements are possible?
- a) 4
- b) 10
- c) 8
- d) 7
Q) How many divisors does 7200 have?
- a) 20
- b) 4
- c) 54
- d) 32
Q) What is the value of M and N respectively? If M39048458N is divisible by 8 & 11; where M & N take integer values from 0 to 9, inclusive?
- a) M = 7; N = 8
- b) M = 8; N = 6
- c) M = 6; N = 4
- d) M = 5; N = 4
Q) What is the remainder when 11^29 is divided by 1332?
- a) 121
- b) 1331
- c) 1211
- d) 1
Number Theory Questions for IPMAT from Previous Year Papers
Solving the previous year's number theory questions for IPMAT is one of the best ways to enhance your preparation.
Try to solve as many previous year question papers as possible to improve your speed.
To ease your preparation, we have provided a few IPMAT number theory questions from last year's IPMAT exam.
Q) What is the remainder when 5^83 is divided by 15?
- a) 1
- b) 5
- c) 3
- d) 0
Q) For what smallest natural number 'n', remainder by 651^n and 652^n when divided by 13 are equal?
- a) 4
- b) 6
- c) 12
- d) 15
Q) What is the remainder when 11^29 is divided by 1332?
- a) 121
- b) 1331
- c) 1211
- d) 1
Q) What is the remainder when 358^76 is divided by 14?
- a) 4
- b) 2
- c) 8
- d) 6
Q) What is the remainder when 65^19-42^19+66^19-43^19 divided by 46?
- a) 45
- b) 1
- c) 0
- d) 44
Q) N is an integer. If (N-5) is a multiple of 13, then the largest number that will always divide (N+8)(N+21) is
- a) 13
- b) 322
- c) 169
- d) 338
Q) Find the last two digits of the number N=199^43.
- a) 09
- b) 99
- c) 89
- d) 19
Read Also - IPMAT Verbal Ability Tips 2027
Q) What is the sum of the first 50 natural numbers?
- A) 1225
- B) 1275
- C) 1325
- D) 1375
Q) If a number is divisible by both 8 and 12, it must also be divisible by:
- A) 16
- B) 24
- C) 32
- D) 36
Q) The unit digit of 7457^{45}745 is:
- A) 1
- B) 3
- C) 7
- D) 9
Q) How many prime numbers are there between 1 and 50?
- A) 12
- B) 15
- C) 16
- D) 10
Q) The least number that should be added to 192 to make it a perfect square is:
- A) 16
- B) 25
- C) 36
- D) 49
Q) What is the remainder when 89 is divided by 7?
- A) 4
- B) 5
- C) 6
- D) 7
Q) The LCM of 18, 24, and 36 is:
- A) 72
- B) 108
- C) 144
- D) 216
Q) The greatest 4-digit number divisible by 12 is:
- A) 9996
- B) 9999
- C) 9992
- D) 9990
Q) The HCF of 72 and 120 is:
- A) 12
- B) 24
- C) 36
- D) 48
Q) If a^b=1024, and both a and b are natural numbers, what is the possible value of (a, b)?
- A) (4, 5)
- B) (8, 3)
- C) (2, 10)
- D) All of the above
Preparation Tips for Number System Questions for IPMAT 2027
The Number System is an essential content category in IPMAT that assesses your ability to understand fundamental number concepts, including divisibility and integer properties.
Knowledge of this material section will boost your examination results.
The following steps will guide your successful completion of the Number Theory Questions for the IPMAT examination:
Master the Basics: Focus on understanding divisibility rules, prime numbers, LCM and HCF, and basic number properties.
Prioritise Key Topics: Concentrate on frequently tested areas such as divisibility, prime numbers, and LCM/HCF calculations.
Practice Regularly: Dedicate time each day to practice and identify your weak spots to strengthen them.
Leverage Previous Year Papers: Solve past papers to familiarise yourself with the IPMAT exam pattern and typical questions.
Take Mock Tests: Regular mock tests help with time management and test-taking strategies while providing insights into areas that need improvement.
Utilise Quality Study Materials: Use comprehensive books and online resources for deeper insights and diverse problem-solving techniques.
Engage in Group Study: Discussing problems in study groups can uncover simpler solutions and boost motivation.
The article offers a targeted guide for preparing number system questions for the IPMAT exam, a critical section that tests a candidate's abilities in number theory.
It outlines strategies to enhance understanding and performance through a mix of theory comprehension, practical exercises, and test simulations.
Check: IPMAT Maths Important Formulas
Key Takeaways:
- Solidify Core Concepts: Ensure a strong grasp of foundational topics such as divisibility, prime numbers, and basic number properties to tackle number system questions effectively.
- Emphasise Important Topics: Focus on areas like divisibility and prime numbers, which are commonly tested, to optimise your study sessions.
- Consistent Practice: Daily practice is essential for developing quick problem-solving skills and identifying and strengthening weak areas.
- Utilise Previous Exams: Solve a number of questions in number theory for IPMAT from previous years' papers to get accustomed to the exam’s format and difficulty level, helping to build confidence and strategy.
- Mock Test Regularly: Engage in full-length IPMAT mock tests to better manage time and refine test-taking strategies while also pinpointing areas needing further review.
Frequently Asked Questions
How can I prepare for the Number Theory Questions for IPMAT 2027?
How can I improve my accuracy while solving number theory questions in the IPMAT 2027 exam?
Which is the best Study Material for IPMAT Quant Preparation?
What types of number theory questions are asked in the IPMAT 2027 exam?
Are number theory questions in IPMAT difficult?
Do number theory questions appear in IPMAT Rohtak & Indore exams?
Lalita Vishwakarma
Content Writer
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