Lesson 1.1: Number System

The Number System is the foundation of arithmetic and includes all types of numbers used in mathematics and daily life. Understanding the number system helps in solving almost every quantitative question in SSC exams.

Types of Numbers

1. Natural Numbers (N): Positive counting numbers starting from 1, 2, 3…
   Example: 1, 2, 3, 4, …

2. Whole Numbers (W): Natural numbers including zero.
   Example: 0, 1, 2, 3, …

3. Integers (Z): Whole numbers and their negatives.
   Example: -3, -2, -1, 0, 1, 2, 3, …

4. Rational Numbers (Q): Numbers that can be expressed as a fraction p/q, where q ≠ 0.
   Example: 1/2, -3/4, 5, 0.

5. Irrational Numbers: Numbers that cannot be expressed as a fraction and have non-terminating, non-repeating decimals.
   Example: √2, π.

6. Real Numbers (R): All rational and irrational numbers together.

Key Properties

• Prime Numbers: Numbers greater than 1 that have only 2 factors: 1 and itself.
  Example: 2, 3, 5, 7, 11, …

• Composite Numbers: Numbers with more than 2 factors.

• Even Numbers: Divisible by 2 (e.g., 2, 4, 6).

• Odd Numbers: Not divisible by 2 (e.g., 1, 3, 5).

Divisibility Rules

• By 2: Last digit is 0, 2, 4, 6, or 8.

• By 3: Sum of digits divisible by 3.

• By 5: Last digit is 0 or 5.

• By 9: Sum of digits divisible by 9.

• By 11: Difference between the sum of digits at odd and even places is divisible by 11 or zero.

Important Concepts

• LCM (Least Common Multiple): Smallest common multiple of two or more numbers.

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

Relation:

$$\text{HCF}\times \text{LCM}=\text{Product of Numbers}$$

Examples

1. Find LCM and HCF of 12 and 18.

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

   • HCF = 2 × 3 = 6

   • LCM = 2² × 3² = 36

Quick Tips for SSC Exams

• Learn prime numbers up to 100.

• Practice LCM & HCF shortcut methods.

• Memorize divisibility rules for quick calculations.