Number System

Overview

The Number System forms the bedrock of primary mathematics and carries significant weight in CG TET Paper I. This topic tests your understanding of how numbers are structured, named, and manipulated—skills essential for teaching Classes 1–5. Expect 3–5 direct questions on whole numbers, integers, place value, factors and multiples.

Mastery here is non-negotiable because nearly every other arithmetic topic (fractions, percentages, mensuration) depends on number sense. Questions range from basic place-value identification to finding LCM/HCF through factor trees, and occasionally include word problems involving divisibility rules. The pedagogy angle may also ask how to teach these concepts to young learners using concrete materials.

Your goal: internalize the definitions, memorize divisibility rules, and practice factor-multiple problems until they become automatic.

Key Concepts

• **Natural Numbers (N)**: Counting numbers starting from 1 → {1, 2, 3, 4, ...}. Zero is NOT included.

• **Whole Numbers (W)**: Natural numbers plus zero → {0, 1, 2, 3, ...}. Every natural number is a whole number, but 0 is only a whole number.

• **Integers (Z)**: Whole numbers extended to include negatives → {..., −3, −2, −1, 0, 1, 2, 3, ...}. The number line extends infinitely in both directions.

• **Place Value vs Face Value**: In 5,847, the digit 8 has face value 8 but place value 800 (8 × 100). Face value never changes; place value depends on position.

• **Factors**: Numbers that divide a given number exactly. Factors of 12 → {1, 2, 3, 4, 6, 12}. Always finite and include 1 and the number itself.

• **Multiples**: Numbers obtained by multiplying a given number by natural numbers. Multiples of 4 → {4, 8, 12, 16, ...}. Always infinite.

• **Prime Numbers**: Numbers with exactly two factors—1 and itself. Examples: 2, 3, 5, 7, 11. Note: 2 is the only even prime; 1 is NOT prime.

• **Composite Numbers**: Numbers with more than two factors. Examples: 4, 6, 8, 9. Note: 1 is neither prime nor composite.

Formulas / Key Facts

**Place Value System (Indian)** | Place | Value | |-------|-------| | Unit | 1 | | Tens | 10 | | Hundreds | 100 | | Thousands | 1,000 | | Ten Thousands | 10,000 | | Lakhs | 1,00,000 | | Ten Lakhs | 10,00,000 | | Crores | 1,00,00,000 |

**Divisibility Rules**

• By 2 → Last digit is 0, 2, 4, 6, or 8
• By 3 → Sum of digits divisible by 3
• By 4 → Last two digits form a number divisible by 4