Lesson 2.1: Number System & Simplification

Objective: Understand the fundamentals of numbers and learn shortcut methods to simplify calculations quickly for Banking Exams.

1. Number System Basics

• Natural Numbers: 1, 2, 3, …

• Whole Numbers: 0, 1, 2, 3, …

• Integers: … -2, -1, 0, 1, 2 …

• Prime Numbers: Numbers greater than 1 with no divisors other than 1 and itself (e.g., 2, 3, 5, 7).

• Composite Numbers: Numbers having more than 2 factors.

• Even & Odd Numbers: Even divisible by 2; Odd not divisible by 2.

• Factors & Multiples:

  • Factors: Numbers that divide a given number exactly.

  • Multiples: Numbers that a given number divides exactly.

• HCF & LCM:

  • HCF (Highest Common Factor): Largest number that divides two or more numbers exactly.

  • LCM (Lowest Common Multiple): Smallest number divisible by two or more numbers.

2. Simplification Techniques

• Use BODMAS/BIDMAS rule: Brackets → Orders (powers, roots) → Division → Multiplication → Addition → Subtraction.

• Shortcut tricks:

  • Split numbers into factors for multiplication/division.

  • Use percentages and fractions in simplified forms for quick calculations.

  • Approximate numbers when allowed to save time.

Examples:

1. Simplify: $25\times 36$

   • Break as $25\times 36=25\times (4\times 9)=(25\times 4)\times 9=100\times 9=900$

2. Find LCM of 12 and 18:

   • Prime factorization: 12 = 2² × 3, 18 = 2 × 3²

   • LCM = 2² × 3² = 36

3. Find HCF of 36 and 60:

   • Prime factorization: 36 = 2² × 3², 60 = 2² × 3 × 5

   • HCF = 2² × 3 = 12

3. Tips for Banking Exams

• Memorize prime numbers up to 100.

• Practice BODMAS questions daily for speed.

• Use factorization and multiplication tricks to solve questions faster.

• Check your answers quickly for mistakes in calculation.

✅ Lesson Summary:
Number System and Simplification form the foundation of Quantitative Aptitude. Mastering factors, multiples, HCF, LCM, and shortcut simplification techniques can save time and improve accuracy in Banking Exams.