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

If you're preparing for CAT 2026, practising CAT Factorials Questions can help you get better at Number System problems. Factorials are used in questions on divisibility, trailing zeroes, highest powers, permutations, combinations, and remainders. These questions may not appear directly in every CAT Paper, but knowing the basic rules can make them easier to solve.

In this guide, you'll find important factorial concepts, formulas, shortcuts, solved examples, and practice questions. You can also use the factorials questions PDF to practise more problems and revise the topic before the CAT exam.

Download FREE Study Material for CAT + OMETs by Supergrads

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?

Direct factorial questions may not appear often in the CAT Exam, but factorials are useful for solving problems from Number System and Modern Mathematics. Knowing the basic concepts can help you solve these questions more easily and save time on tricky Quant problems.

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.

Download CAT Previous Year Papers For Practise

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)!]

Check Full Details About CAT 2026 Syllabus

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

Attempt Free Mock 2026 Test Series by Supergrads

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

Keep these points in mind when solving factorial questions so you don't lose marks over small errors.

• Calculating the full factorial: Avoid finding the complete value unless the question asks for it. Expand only the terms required.
• Counting zeroes incorrectly: For trailing zeroes, count how many times 5 is a factor in the factorial.
• Ignoring common factors: Check the numerator and denominator for terms that can be cancelled.
• Using the wrong formula: For the highest power of a prime number in a factorial, divide by its successive powers and add the quotients.
• Not checking the answer: Go through your calculations once before marking the final option.

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

Along with studying from books, make time to practise Factorials Questions online. You can also use CAT online coaching for guided practice and regular tests. Solve questions topic-wise and revise the formulas with a CAT factorials questions PDF. Here are a few resources that can help you practise:

• CAT Previous Year Papers to practise questions from past exams.
• Quantitative Aptitude mock tests to check your speed and accuracy.
• Number System questions to practise factorials and related concepts.
• Daily Quant practice to get more comfortable with different types of questions.
• CAT factorials questions PDF to revise formulas and solve a few questions before mock tests.

Experts Preparation Tips for CAT 2026

Use these tips to get better at Factorials Questions for CAT:

• Learn the basic factorial rules before moving to difficult questions.
• Practise breaking factorials into smaller parts instead of calculating the full value.
• Remember the formulas for finding trailing zeroes and the highest power of a number in a factorial.
• Solve at least 20 Number System questions every week.
• Keep revising the formulas with the help of a CAT factorials questions PDF.
• Check your mistakes after each sectional mock test and try to understand where you went wrong.
• Focus on understanding how a question works instead of memorising its solution.

Expert Tip: In CAT, you can often save time by simplifying a question instead of doing lengthy calculations. Look for factorial patterns and use the basic Number System rules to find the answer quickly.

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.

Practising factorial questions regularly, taking mock tests, and revising with a CAT factorials questions PDF can help you get better at Quant. As you continue your CAT preparation, you'll become more comfortable with these questions and learn to solve them in less time.