CAT Factorials Question 2026: Concepts, Formula Sheet, Tricks, Practice Questions & PDF

Overview: If you're preparing for CAT 2026, mastering CAT Factorials Questions is essential for strengthening your Number System concepts. Although factorials may not appear as a standalone topic every year, they frequently form the basis of questions involving divisibility, trailing zeroes, highest powers, combinations, permutations, and remainders. A clear understanding of factorial properties can help you solve these questions quickly and accurately.

In this comprehensive guide, you'll learn everything about Factorials Questions, including important concepts, formulas, shortcuts, solved examples, preparation strategies, and practice questions. You'll also discover how a factorials questions PDF can help you revise efficiently before the exam.

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Quick Answer: Factorials Questions assess your understanding of factorial notation, divisibility, trailing zeroes, highest powers of prime numbers, and Number System concepts. These questions are generally solved using logical reasoning and mathematical properties rather than lengthy calculations. Practising a CAT factorials questions PDF regularly is one of the best ways to improve speed and accuracy in CAT Quant.

Key Takeaways

• Factorials Questions are part of the Number System topic.
• Understand factorial notation and its mathematical properties.
• Learn shortcuts for trailing zeroes and highest power questions.
• Practise previous year CAT questions regularly.
• Revise using a CAT factorials questions PDF before sectional and full-length mocks.

Table of Contents

1. What are CAT Factorials Questions 2026?
2. Why are Factorials Questions Important for CAT 2026?
3. Factorials Questions Syllabus
4. Important Factorial Concepts You Must Know
5. Important Formulas for Factorials Questions
6. Types of Factorials Questions in CAT
7. Step-by-Step Strategy to Solve Factorials Questions for CAT
8. 30 Factorials Questions in CAT with Answers
9. Previous Year CAT Factorials Questions
10. Common Mistakes While Solving Factorials Questions for CAT
11. Best Books for Factorials Questions
12. Best Online Resources and CAT Factorials Questions PDF
13. Expert Preparation Tips
14. One-Week Preparation Plan
15. Conclusion

What are CAT Factorials Questions 2026?

The Factorials Questions are Number System problems based on the mathematical operation called a factorial, represented by the symbol !. The factorial of a positive integer is the product of all positive integers less than or equal to that number.

For example:

• 5! = 5 × 4 × 3 × 2 × 1 = 120
• 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040
• 0! = 1

In CAT, factorials are rarely tested through direct computation. Instead, they are used in problems involving divisibility, highest powers, trailing zeroes, combinations, permutations, and remainders. Therefore, understanding the logic behind Factorials Questions for CAT is more important than memorising values.

Why are CAT Factorials Questions Important for CAT 2026?

Although the number of direct factorial questions in CAT exam 2026 is limited, the concepts are widely used across Number System and Modern Mathematics topics. Mastering Factorials Questions improves logical reasoning and helps solve several advanced Quant problems efficiently.

Benefit	Importance for CAT Preparation
Strengthens Number System Concepts	Builds a strong mathematical foundation.
Improves Logical Thinking	Enhances analytical problem-solving skills.
Useful in Multiple Topics	Applicable in permutations, combinations, divisibility, and remainders.
Boosts Speed	Shortcut techniques reduce lengthy calculations.
High ROI Topic	A few concepts help solve several CAT-level questions.

Factorials Questions Syllabus In CAT

There is no separate chapter for factorials in the CAT syllabus. However, Factorials Questions in CAT 2026 are included under Number System and frequently appear alongside related mathematical concepts.

• Factorial Notation
• Properties of Factorials
• Trailing Zeroes
• Highest Power of a Prime in n!
• Divisibility Using Factorials
• Remainders
• Permutations and Combinations
• Basic Number Theory

Aspirants should regularly practise Factorials Questions for CAT along with Number System topics to improve conceptual understanding and problem-solving speed.

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Important Factorial Concepts You Must Know

Before solving Factorials Questions, you should understand the core concepts that frequently appear in CAT Quant. A strong grasp of these fundamentals will help you solve questions involving Number Systems, divisibility, permutations, and combinations with ease.

1. What is a Factorial?

The factorial of a positive integer n is the product of all positive integers from 1 to n. It is represented using the symbol !.

Formula:

n! = n × (n − 1) × (n − 2) × ... × 2 × 1

Examples:

• 3! = 3 × 2 × 1 = 6
• 5! = 120
• 8! = 40,320
• 10! = 36,28,800

Special Case:

• 0! = 1

This concept forms the foundation of many Factorials Questions for CAT.

2. Properties of Factorials

Understanding factorial properties makes calculations much faster during the exam.

Property	Expression
Recursive Property	n! = n × (n − 1)!
Zero Factorial	0! = 1
Factorial Division	n! / (n − 1)! = n
Expansion	n! = n × (n − 1) × (n − 2)...

3. Highest Power of a Prime in n!

This is one of the most frequently tested concepts in CAT Factorials Questions 2026.

To determine the highest power of a prime number p present in n!, use the following formula:

Highest Power = ⌊n/p⌋ + ⌊n/p²⌋ + ⌊n/p³⌋ + ...

Example:

Find the highest power of 5 in 100!.

Calculation:

• ⌊100/5⌋ = 20
• ⌊100/25⌋ = 4
• ⌊100/125⌋ = 0

Total = 20 + 4 = 24

Therefore, the highest power of 5 in 100! is 24.

4. Trailing Zeroes in Factorials

Trailing zero questions are among the easiest scoring questions in Factorials Questions.

The number of trailing zeroes depends on the number of times the factor 10 = 2 × 5 appears. Since there are always more 2s than 5s in factorials, we simply count the powers of 5.

Formula:

Trailing Zeroes = ⌊n/5⌋ + ⌊n/25⌋ + ⌊n/125⌋ + ...

Example:

Find the number of trailing zeroes in 50!.

• ⌊50/5⌋ = 10
• ⌊50/25⌋ = 2

Total = 12 trailing zeroes.

5. Divisibility Using Factorials

Several Factorials Questions for CAT test whether one factorial divides another expression exactly.

Example:

Does 8! divide 10!?

Since:

10! = 10 × 9 × 8!

Therefore, 8! completely divides 10!.

6. Factorials in Permutations and Combinations

Factorials are widely used in Modern Mathematics.

Permutation Formula:

nPr = n! / (n − r)!

Combination Formula:

nCr = n! / [r! × (n − r)!]

Although these topics are studied separately, factorial concepts are essential for solving them efficiently.

Important Formulas for CAT 2026 Factorials Questions 

Remembering these formulas will help you solve Factorials Questions much faster during the exam.

Concept	Formula
Factorial	n! = n × (n − 1)!
Zero Factorial	0! = 1
Trailing Zeroes	⌊n/5⌋ + ⌊n/25⌋ + ...
Highest Power of Prime	⌊n/p⌋ + ⌊n/p²⌋ + ...
Permutation	nPr = n! / (n − r)!
Combination	nCr = n! / [r! (n − r)!]

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Types of CAT 2026 Factorials Questions

Factorials Questions can appear in multiple formats. Recognising the question type helps you apply the correct concept quickly.

1. Basic Factorial Questions

These questions test your understanding of factorial notation and simple calculations.

Example:

Evaluate 7! / 5!

Solution:

7! / 5! = 7 × 6 = 42

2. Trailing Zero Questions

These require finding the number of zeroes at the end of a factorial.

Example:

How many trailing zeroes are there in 75!?

Solution:

• ⌊75/5⌋ = 15
• ⌊75/25⌋ = 3

Total = 18

3. Highest Power Questions

These questions ask for the highest exponent of a prime factor present in a factorial.

Example:

Find the highest power of 2 in 20!.

Apply the highest power formula to obtain the answer efficiently.

4. Divisibility Questions

These questions determine whether one factorial completely divides another number or expression.

5. Remainder-Based Questions

These involve finding the remainder after dividing factorial expressions by a given number using Number System concepts.

6. Combination and Permutation Questions

These problems require simplifying factorial expressions while solving permutations and combinations. Mastering factorial properties significantly reduces computation time.

Step-by-Step Strategy to Solve Factorials Questions for CAT

Follow this systematic approach to solve Factorials Questions for CAT quickly and accurately.

1. Identify the type of factorial problem.
2. Expand only the required factorial terms instead of calculating the complete value.
3. Cancel common factors wherever possible.
4. Apply the appropriate formula for trailing zeroes or highest powers.
5. Verify the final answer before moving to the next question.

With regular practice and revision using a CAT factorials questions PDF, you can solve these questions in under a minute during the CAT exam.

30 Factorials Questions In CAT with Answers

Practising a variety of Factorials Questions is the best way to improve conceptual clarity and speed. The questions below cover the most frequently tested concepts, including factorial expansion, trailing zeroes, divisibility, highest powers, and simplification. You can also revise these questions later using a CAT factorials questions PDF.

Basic Level Questions

No.	Question	Answer
1	Find the value of 5!.	120
2	Evaluate 7! ÷ 5!.	42
3	What is 0!?	1
4	Evaluate 8! ÷ 6!.	56
5	Find 6! ÷ 3!.	120
6	Find the value of 9! ÷ 8!.	9
7	Evaluate 10! ÷ 9!.	10
8	What is the value of 4!?	24
9	Evaluate 11! ÷ 10!.	11
10	Find 12! ÷ 11!.	12

Intermediate Level Questions

No.	Question	Answer
11	How many trailing zeroes are there in 25!?	6
12	How many trailing zeroes are there in 50!?	12
13	Find the highest power of 5 in 100!.	24
14	Find the highest power of 2 in 10!.	8
15	Does 8! divide 10! exactly?	Yes
16	Find the number of trailing zeroes in 100!.	24
17	Evaluate 9! ÷ (7! × 2!).	36
18	Evaluate 10! ÷ (8! × 2!).	45
19	Find the highest power of 3 in 27!.	13
20	Find the highest power of 2 in 16!.	15

CAT-Level Practice Questions

No.	Question	Answer
21	Find the remainder when 10! is divided by 9.	0
22	Find the number of digits in 10!.	7
23	Evaluate 12! ÷ (10! × 2!).	66
24	Evaluate 13! ÷ 12!.	13
25	Find the highest power of 5 in 125!.	31
26	How many trailing zeroes are there in 200!?	49
27	Evaluate 14! ÷ 13!.	14
28	Find the value of 15! ÷ 14!.	15
29	Find the highest power of 2 in 25!.	22
30	How many trailing zeroes are there in 75!?	18

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Previous Year Factorials Questions Trend In CAT

Although Factorials Questions are not asked as standalone questions every year, factorial concepts frequently appear in Number System, divisibility, and permutation-combination problems. A solid understanding of factorial properties enables candidates to solve these questions quickly.

CAT Year	Question Type	Difficulty Level
CAT 2025	Number System with factorial concepts	Moderate
CAT 2024	Highest power and divisibility	Moderate
CAT 2023	Permutation and Combination using factorials	Moderate
CAT 2022	Factorial simplification	Easy to Moderate
Earlier CAT Papers	Trailing zeroes and Number System	Easy

Practising previous year questions along with a CAT factorials questions PDF will help you recognise recurring concepts and improve your exam readiness.

Common Mistakes While Solving Factorials Questions for CAT

Many aspirants lose marks in Factorials Questions for CAT due to avoidable conceptual errors. Being aware of these mistakes can significantly improve your accuracy.

Common Mistake	How to Avoid It
Calculating complete factorial values	Expand only the required terms instead of evaluating the entire factorial.
Incorrect trailing zero calculation	Always count powers of 5, not 10.
Ignoring factorial properties	Use cancellation techniques wherever possible.
Using incorrect highest power formula	Apply ⌊n/p⌋ + ⌊n/p²⌋ + ... correctly.
Making calculation mistakes	Verify intermediate steps before selecting the final answer.

Best Books for Factorials Questions

The following CAT books provide excellent conceptual explanations and practice exercises for Factorials Questions.

Book	Why You Should Read It
How to Prepare for Quantitative Aptitude for CAT by Arun Sharma	Detailed Number System theory with CAT-level practice questions.
Quantitative Aptitude for CAT by Nishit K. Sinha	Excellent conceptual explanations and advanced problems.
Quantitative Aptitude by Sarvesh K. Verma	Ideal for strengthening Number System fundamentals.
Previous Year CAT Papers	Understand actual CAT question trends and difficulty level.

Best Online Resources and CAT Factorials Questions PDF

Online practice is equally important for mastering Factorials Questions. Along with books, candidates should solve topic-wise practice sheets and revise regularly using a CAT factorials questions PDF.

Recommended resources include:

• Previous Year CAT Question Papers
• Sectional Quantitative Aptitude Mock Tests
• Topic-wise Number System Practice Sets
• Daily Quant Practice Questions
• CAT factorials questions PDF for quick revision before mocks.

Expert Preparation Tips

Use these expert tips to improve your performance in Factorials Questions:

• Master factorial properties before attempting advanced questions.
• Practise expanding factorial expressions instead of calculating their complete values.
• Memorise formulas for trailing zeroes and highest powers.
• Solve at least 20 Number System questions every week.
• Revise formulas regularly using a CAT factorials questions PDF.
• Analyse mistakes after every sectional mock test.
• Focus on understanding concepts rather than memorising solutions.

How To Prepare For CAT 2026 In 5 Months

One-Week Preparation Plan

Day	Preparation Goal
Day 1	Learn factorial notation and basic properties.
Day 2	Practice trailing zeroes and highest power concepts.
Day 3	Solve divisibility and factorial simplification problems.
Day 4	Practice permutation and combination questions involving factorials.
Day 5	Attempt a Number System sectional test.
Day 6	Analyse mistakes and revise important formulas.
Day 7	Revise using a CAT factorials questions PDF and solve previous year CAT questions.

Conclusion

Factorials Questions in CAT form an important part of Number System preparation and frequently appear in questions involving divisibility, highest powers, permutations, combinations, and trailing zeroes. Instead of memorising large factorial values, aspirants should focus on understanding the underlying concepts, recognising patterns, and applying shortcut techniques.

Regular practice, mock tests, and revision through a CAT factorials questions PDF will strengthen your problem-solving skills and improve your performance in the Quantitative Aptitude section. With consistent CAT preparation and concept-based learning, solving Factorials Questions for CAT becomes significantly easier and more time-efficient.