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IPMAT Number System Questions 2026
IPMAT Number System questions are an important part of the IPMAT Quant section. These questions check your understanding of basic number concepts. These topics include divisibility, factors, multiples, remainders, HCF, LCM, unit digit, and integers.
In the exam, Number System questions may be asked directly or as part of word problems. The good thing is that these questions become easy when your basics are clear. You do not need very difficult maths. You only need to understand the concepts, remember the rules, and practice regularly.
In this blog, you will get a simple formula PDF, practice questions with answers, and some extra questions for self-practice. You will also learn about common mistakes students make and some easy tips to solve questions faster in the exam.
Important Formulas for IPMAT Number System Questions
You only need a few basic formulas and rules to solve most Number System questions in IPMAT. These formulas help you solve questions based on divisibility, factors, remainders, HCF, LCM, and digits.
You can download the full formula PDF from the link above. Here is a quick look at some important formulas and rules:
Concept | Formula / Rule |
Even Number | A number that is divisible by 2 |
Odd Number | A number that is not divisible by 2 |
Divisibility by 2 | Last digit must be 0, 2, 4, 6, or 8 |
Divisibility by 3 | Sum of digits must be divisible by 3 |
Divisibility by 5 | Last digit must be 0 or 5 |
Divisibility by 9 | Sum of digits must be divisible by 9 |
Divisibility by 10 | Last digit must be 0 |
Divisibility by 11 | Difference of the sum of alternate digits must be 0 or divisible by 11 |
HCF | Greatest common factor of two or more numbers |
LCM | Smallest common multiple of two or more numbers |
Relation between HCF and LCM | Product of two numbers = HCF × LCM |
Remainder Formula | Dividend = Divisor × Quotient + Remainder |
Number of Factors | If N = p^a × q^b × r^c, then total factors = (a+1)(b+1)(c+1) |
Co-prime Numbers | Two numbers having HCF = 1 |
Unit Digit | The last digit of a number |
Integers | Positive numbers, negative numbers, and 0 |
These formulas and rules are very useful for solving Number System questions in IPMAT.
Top 5 Common Mistakes to Avoid in IPMAT Number System Questions
Forgetting divisibility rules
You should remember the divisibility rules of numbers like 2, 3, 5, 9, and 11.
Not using prime factorization
Many questions become easy when you first break the number into prime factors.
Mistakes in remainder questions
Use the remainder formula carefully and check your answer again.
Confusing HCF and LCM
Many students mix up HCF and LCM. Learn clearly where to use each one.
Calculation mistakes
Sometimes the method is correct, but small mistakes in addition, multiplication, or division give the wrong answer. Solve slowly and step by step.
List of IPMAT Number System Questions
Here is a short set of IPMAT-style Number System questions for practice. These questions cover common topics like divisibility, factors, multiples, remainders, HCF, LCM, and unit digits. Practice these questions regularly to improve your speed and accuracy for the IPMAT exam.
Question 1
The number of positive integers which divide (1890)*(130)*(170) and are not divisible by 45 is ____________.
correct answer:- 320
Question 2
The highest possible value of the ratio of a four digit number and the sum of its four digits is:
correct answer:- 1
Question 3
Placing which of the following two digits at the right end of 4530 makes the resultant six digit number divisible by 6,7 and 9?
correct answer:- 1
Question 4
The unit digit in $$(743)^{85} −(525)^{37} + (987)^{96}$$ IS ________
correct answer:- 1
Question 5
The number of factors of 1800 that are multiple of 6 is:
correct answer:- 18
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Question 6
You have been asked to select a positive integer N which is less than 1000 , such that it is either a multiple of 4, or a multiple of 6, or an odd multiple of 9. The number of such numbers is
correct answer:- 388
Question 7
Which of the following numbers is divisible by $$3^{10} + 2$$
correct answer:- 4
Question 8
The number of factors of $$3^5 \times 5^8 \times 7^2$$ that are perfect squares is
correct answer:- 30
Question 9
Let p be a positive integer such that the unit digit of $$p^{3}$$ is 4. What are the possible unit digits of $$(p+3)^{3}$$?
correct answer:- 1
Question 10
When the square of the difference of two natural numbers is subtracted from the square of the sum of the same two numbers and the result is divided by four, we get
correct answer:- 2
Question 11
The maximum value of the natural number n for which $$21^{n}$$ divides 50! is
correct answer:- 3
Question 12
Determine the greatest number among the following four numbers
correct answer:- 2
Question 13
In a four-digit number, the product of the thousands digit and the units digit is zero, while their difference is 7. The product of the middle digits is 18. The thousands digit is as much more than the units digit as the hundreds digit is more than the tens digit. The four-digit number is _____________.
correct answer:- 7920
Question 14
The remainder when $$11^{1011} + 1011^{11}$$ is divided by 9 is
correct answer:- 2
Question 15
In a division problem, product of quotient and the remainder is 24 while their sum is 10. If the divisor is 5 then dividend is__________.
correct answer:- 34
Question 16
The remainder when $$(29^{29})^{29}$$ is divided by 9 is
correct answer:- 2
Question 17
How many different numbers can be formed by using only the digits 1 and 3 which are smaller than 3000000?
correct answer:- 3
Question 18
The remainder when 1! + 2! + 3! +∙∙∙+95! is divided by 15 is _____________.
correct answer:- 3
Question 19
The number of pairs of integers whose sums are equal to their products is
correct answer:- 2
Question 20
If the five-digit number abcde is divisible by 6, then which of the following numbers is not necessarily divisible by 6?
correct answer:- 2
