There are ten digits in the number system (0,1,2,3,4,5,6,7,8,9). When these digits are added together, a number is formed. Understanding these digits is important for solving number system questions for CLAT.
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If you are preparing for CLAT 2027, mastering Number System Questions for CLAT can help improve your speed, calculation accuracy, and overall performance in the Quantitative Techniques section.
Number System Questions For CLAT 2027
Place Value refers to how the value of a digit changes depending on its position; meanwhile, Face Value refers to how a digit’s value remains constant regardless of its position.
On this topic, you can expect 2-3 questions on the CLAT exam. Even though it is the least important section of the exam, if you prepare well, you can earn a perfect score.
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Number System Questions for CLAT with Answers
Question: Which of the following is a prime number?
A. 9
B. 15
C. 17
D. 21
Answer: C. 17
Explanation: 17 has only two factors, 1 and 17. Hence, it is a prime number.
Question: What is the HCF of 24 and 36?
A. 6
B. 8
C. 12
D. 18
Answer: C. 12
Explanation: The common factors of 24 and 36 are 1, 2, 3, 4, 6 and 12. The highest common factor is 12.
Question: What is the LCM of 8 and 12?
A. 16
B. 24
C. 32
D. 48
Answer: B. 24
Explanation: Multiples of 8 are 8, 16, 24, 32. Multiples of 12 are 12, 24, 36. The least common multiple is 24.
Question: Which number is divisible by 9?
A. 234
B. 245
C. 256
D. 287
Answer: A. 234
Explanation: Sum of digits of 234 is 2 + 3 + 4 = 9. Since 9 is divisible by 9, 234 is divisible by 9.
Question: What is the remainder when 47 is divided by 5?
A. 0
B. 1
C. 2
D. 3
Answer: C. 2
Explanation: 47 = 5 × 9 + 2. Therefore, the remainder is 2.
Question: How many factors does 16 have?
A. 3
B. 4
C. 5
D. 6
Answer: C. 5
Explanation: The factors of 16 are 1, 2, 4, 8 and 16.
Question: Which of the following is an irrational number?
A. 1/2
B. 3/4
C. √2
D. 5/8
Answer: C. √2
Explanation: √2 cannot be expressed in the form p/q, where q is not equal to 0. Hence, it is irrational.
Question: The sum of two odd numbers is always:
A. Odd
B. Even
C. Prime
D. Composite
Answer: B. Even
Explanation: For example, 3 + 5 = 8 and 7 + 9 = 16. The sum of two odd numbers is always even.
Question: Which is the smallest prime number?
A. 0
B. 1
C. 2
D. 3
Answer: C. 2
Explanation: 2 is the smallest prime number and the only even prime number.
Question: A number is divisible by 6 if it is divisible by:
A. 2 only
B. 3 only
C. 2 and 3
D. 2 and 5
Answer: C. 2 and 3
Explanation: A number is divisible by 6 only when it is divisible by both 2 and 3.
Various Types of Number System Questions For CLAT 2027
Among the other topics, the number system is the simplest because it covers basic operations and issues. You can address a higher degree of application-based challenges with the help of these fundamentals.
The following are various types of numbers about which you can anticipate questions on the upcoming exam:
- Natural Numbers: Natural Numbers are positive numbers (1,2,3,4,5,6,…) that can be numbered starting at 1. Positive integers are another name for these numbers.
- Whole Numbers: Whole Numbers are all the numbers that can be numbered, including zero (0,1,2,3,4,…).
- Integers: Integers are all positive and negative numbers that can be counted, including zero. … -3,-2,-1,0,1,2,3…. Positive integers are positive numbers, including zero, one, two, three, and so on. Negative Integers are negative numbers…. -4,-3,-2,-1.
- Rational Number: A number that may be written as (a/b), where b≠0 is a rational number. All integers, including zero and fractions, are included.
- Co-Prime Numbers are two numbers that have the same HCF, i.e., there is no other common factor between them. 5 and 24 are two examples.
- Irrational Numbers: Irrational numbers are those that cannot be stated in the standard (a/b) format. As an example, π = 1415926535897932384626433832795028… We use 3.14 or 22/7 (where 22/7 is an irrational number) because this value of pi never ends. Irrational numbers are also recognized for having a recurrent feature.
- Even numbers: Even numbers are positive and negative integers that may be divided by two.
- Odd Numbers: Odd numbers are those that can’t be divided by two.
- Prime Numbers: Prime numbers are positive integers with only two factors: 1 and themselves. It’s a good idea to memorise all 25 prime numbers below 100, which are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.
- Composite Numbers: All the numbers that are not prime are Composite Numbers.
- Real Number: The term “real number” encompasses all of the numbers covered thus far. The number line can be used to represent these figures.
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How to Attend Number System Questions for CLAT 2027?
Most of the students will be probably wondering how to rapidly solve number system questions in the exam.
Here are a few pointers to assist you in better understanding how to do CLAT Maths Questions in a flash.
- There are passages and questions throughout the entire question paper. As a result, it is critical to read the entire sentence carefully.
- Before you answer any question, make sure you understand every phrase.
- The exam conducting authority is examining your ability to solve logical questions rather than only formula-based questions, as the question paper pattern changes each year. As a result, it is critical to set aside at least one hour per day for CLAT Maths preparation.
- Make sure to keep track of any calculations you make on the rough sheet during the exam.
- As the questions are comprehension-based, you may need to refer back to the prior response to solve the following one.
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Sample Questions based on the number system of the CLAT exam
- What is the value of x that makes 7396×51 divisible by 11? 9?
- What should be deducted from 2016 for it to be divisible by 19 completely?
- Find the product’s unit digit (463 * 756 * 414 * 679).
- How many prime factors are there in (47 * 75 *1111)?
- What is the natural number that is closest to 8488 and is divisible by 77?
- Find the smallest number that can be subtracted from 13501 to leave a divisible by 87 residual.
- What is the smallest five-digit number divisible by 31?
- What is the greatest five-digit number divisible by 91?
- When you divide a number by 56, the remaining is 29. If the same number is divided by 8, what is the remainder?
- Determine how many numbers in the range of 100 to 1000 are divisible by six.
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Why are Number System Questions Important for CLAT?
Number Systems form the base of several Quantitative Techniques topics.
A strong understanding of Number Systems helps in:
- Faster calculations
- Better approximation skills
- Improved Data Interpretation performance
- Reduced calculation errors
- Stronger arithmetic fundamentals
Many topics such as percentages, averages, profit and loss, ratio and proportion, and simple interest rely on Number System concepts.
Important Divisibility Rules for CLAT
| Number | Divisibility Rule |
|---|---|
| 2 | The last digit is even |
| 3 | The sum of digits is divisible by 3 |
| 4 | The last two digits are divisible by 4 |
| 5 | The number ends in 0 or 5 |
| 6 | The number is divisible by both 2 and 3 |
| 8 | The last three digits are divisible by 8 |
| 9 | The sum of digits is divisible by 9 |
| 10 | The number ends in 0 |
Key Number System Concepts for CLAT
1. Factors and Multiples
A factor is a number that divides another number exactly. A multiple is the product obtained when a number is multiplied by another number.
Example: Factors of 12 are 1, 2, 3, 4, 6 and 12. Multiples of 12 are 12, 24, 36, 48 and so on.
2. Prime and Composite Numbers
A prime number has exactly two factors: 1 and itself. A composite number has more than two factors.
Example: 2, 3, 5, 7 and 11 are prime numbers. 4, 6, 8, 9 and 12 are composite numbers.
3. HCF and LCM
HCF stands for Highest Common Factor. It is the largest number that divides two or more numbers exactly. LCM stands for Least Common Multiple. It is the smallest number that is a common multiple of two or more numbers.
Example: HCF of 12 and 18 is 6. LCM of 12 and 18 is 36.
4. Remainders
Remainder-based questions test what is left after division. The basic relation is:
Dividend = Divisor × Quotient + Remainder
Example: When 25 is divided by 4, the remainder is 1 because 25 = 4 × 6 + 1.
How Number System Appears in CLAT Quantitative Techniques
In CLAT, number system questions may not always appear as direct standalone questions. They are often included within data interpretation sets or arithmetic-based passages. For example, a table may contain sales figures, student counts, vote shares, or financial data, and you may need number system concepts to identify factors, calculate ratios, find differences, or interpret patterns.
This is why candidates should not study Number System only as a theory topic. You should practise applying these concepts in mixed quantitative sets.
Common Mistakes in Number System Questions for CLAT
1. Confusing Prime and Composite Numbers
Many students wrongly treat 1 as a prime number. Remember that 1 is neither prime nor composite.
2. Ignoring Divisibility Rules
Students often waste time performing long division when simple divisibility rules can give the answer quickly.
3. Making Calculation Errors
Even easy questions can go wrong due to careless addition, subtraction or multiplication. Always double-check basic calculations.
4. Mixing HCF and LCM
HCF is the greatest common factor, while LCM is the smallest common multiple. Read the question carefully before solving.
5. Spending Too Much Time on One Question
CLAT is a time-bound exam. If a number system question is taking too long, mark it and move ahead.
Frequently Asked Questions (FAQs)
Q: What are the finest books to use to prepare for the CLAT Maths Section?
A: To prepare for the CLAT Exam, you must carefully select the books that will be most beneficial to your studies. The following are some of the top books for CLAT Maths Section preparation: Pearson's Quantitative Aptitude, Arihant's First Track Objective Arithmetic, and Pearson's Maths 30 Days Wonder S. Chand, Samiksha Gupta and R.K. Gupta's Legal Aptitude Test (CLAT).
Q: What can I do to improve my CLAT Maths Section performance?
A: Following the expert advice will undoubtedly assist you in better preparing for the CLAT Maths 2027. Begin your preparation by studying from the correct books that cover all of the concepts and topics according to the most recent exam pattern, and make sure you are familiar with the CLAT Exam's full Paper Pattern and Syllabus before you begin.
Q: What is the total number of Questions on the Number System asked in the CLAT exam?
A: CLAT Number System Questions are a prevalent topic that should not be ignored during preparation. This topic is likely to generate 1-2 questions in general. For the CLAT Questions on Number System, candidates should practice thoroughly and be well-versed in all relevant topics.
Q: What are some tips for CLAT Maths Preparation?
A: The following are some general preparation ideas for the Maths section: Make an effort to comprehend the concepts of the topics. Do not attempt to cram. On the last day of preparation, don't try to dig into any new topics. Re-examine the previous themes. Examine the formulas and put them to use. Check for shortcuts as well during your preparation.