Number System
TN TET Mathematics
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Overview
The Number System forms the backbone of primary mathematics and is a foundational topic for TN TET Paper I and Paper II. Questions from this topic test your understanding of whole numbers, integers, place value, divisibility rules, and finding HCF and LCM. Expect 3–5 direct questions, plus this knowledge underpins fractions, algebra, and word problems.
Mastery here means quick mental calculations during the exam. You must be fluent with divisibility tests (saves time on HCF/LCM problems), comfortable moving between number types, and confident with place value manipulation. Pedagogy questions may also ask how to teach these concepts to children—connecting abstract numbers to concrete understanding.
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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.
- **Integers (Z)**: Whole numbers plus negative numbers. {..., -3, -2, -1, 0, 1, 2, 3, ...}. Includes positive integers, negative integers, and zero.
- **Place Value vs Face Value**: Face value is the digit itself. Place value = digit × position value. In 4,725: the face value of 7 is 7, but its place value is 700.
- **Divisibility**: A number is divisible by another if the remainder is zero. Divisibility rules provide shortcuts without actual division.
- **Factors and Multiples**: Factors divide a number exactly. Multiples are products of a number with natural numbers. 12's factors: 1, 2, 3, 4, 6, 12. 12's multiples: 12, 24, 36...
- **HCF (Highest Common Factor)**: The largest number that divides two or more numbers exactly. Also called GCD.
- **LCM (Lowest Common Multiple)**: The smallest number that is a multiple of two or more numbers.
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Formulas / Key Facts
**Place Value System (Indian)** | Place | Value | |-------|-------| | Units | 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 is divisible by 3
- **By 4**: Last two digits form a number divisible by 4
- **By 5**: Last digit is 0 or 5
- **By 6**: Divisible by both 2 and 3