Number System
📋 Quick-reference guides with key formulas and must-know concepts. Perfect for daily practice, last-minute revision, and on-the-go learning.
Cheat Sheets
Study MaterialNumber System Cheat Sheet
The Number System is one of the most important topics in Quantitative Aptitude and is frequently asked in SSC, Banking, Railway, UPSC, Defence, Insurance, CAT, and other competitive examinations.
This cheat sheet helps candidates understand different categories of numbers, divisibility rules, factors and multiples, LCM and HCF, remainders, unit digits, trailing zeros, and number base systems.
About This Cheat Sheet
Complete guide to Number System for competitive exams covering:
Types of Numbers
Natural, Whole, Integers, Rational, Irrational, Real, Prime, Composite, Even, Odd, and Co-prime Numbers.
Divisibility Rules
- 2 → Last digit even
- 3 → Sum divisible by 3
- 5 → Ends with 0 or 5
- 9 → Sum divisible by 9
- 11 → Alternate sum rule
LCM & HCF
- LCM × HCF = Product
- Prime Factorization
- Euclid Division Method
- Shortcut Tricks
Remainders & Modulus
Important remainder theorem concepts and modular arithmetic basics.
Unit Digit Tricks
- Powers of 2 → 2,4,8,6
- Powers of 7 → 7,9,3,1
- Cyclic Patterns
- Fast Calculations
Base Number Systems
- Binary
- Octal
- Decimal
- Hexadecimal
Trailing Zeros
Shortcut methods to calculate zeros in factorial-based questions.
Important Formulas
Exam-focused formulas, tricks, and solved examples for quick revision.
Topics Covered
| Topic | Description |
|---|---|
| Natural Numbers | Counting numbers starting from 1 |
| Whole Numbers | Natural numbers including 0 |
| Integers | Positive, negative, and zero values |
| Rational Numbers | Numbers represented in p/q form |
| Irrational Numbers | Non-terminating and non-repeating numbers |
| Prime Numbers | Numbers having exactly two factors |
| Composite Numbers | Numbers having more than two factors |
| Divisibility Rules | Shortcut divisibility techniques |
| LCM & HCF | Methods and formulas for calculation |
| Remainders | Remainder theorem and cyclicity concepts |
| Unit Digit | Last digit calculation shortcuts |
| Trailing Zeros | Zeros in factorial and multiplication problems |
| Base Systems | Binary, Octal, Decimal, Hexadecimal systems |
Why This Cheat Sheet is Important
Build Strong Basics
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Improve Calculation Speed
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Apply Shortcut Techniques
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Solve Questions Faster
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Score Better in Exams
Competitive Exams Covered
- SSC CGL
- SSC CHSL
- Bank PO & Clerk
- Railway Exams
- UPSC CSAT
- Defence Exams
- Insurance Exams
- State Government Exams
- MBA Entrance Exams
Quick Example
Example:
Find the unit digit of 745
Pattern of unit digits for powers of 7:
7 → 9 → 3 → 1 → Repeat
45 ÷ 4 leaves remainder 1
Therefore, unit digit = 7
Answer = 7
Final Takeaway
This Number System Cheat Sheet provides complete revision material for all major concepts frequently asked in competitive examinations. Regular practice of formulas, divisibility rules, remainder concepts, and unit digit tricks can significantly improve speed, accuracy, and problem-solving ability.
It is highly useful for quick revision before exams and helps candidates strengthen the foundation of Quantitative Aptitude.
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Complete Quick Revision Material for Competitive Exams
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