Number System

Overview

The Number System forms the bedrock of primary mathematics and carries significant weightage in OTET Paper I. Questions from this topic test your understanding of how numbers are built, classified, and related to each other. Mastery here directly supports performance in fractions, decimals, LCM-HCF, and word problems.

For the exam, you must be comfortable with the hierarchy of number types (natural → whole → integers), place value concepts up to crores, and the relationship between factors and multiples. Most questions are straightforward calculations or concept-based MCQs, but careless errors in place value or confusing factors with multiples cost marks.

Focus on building a clear mental model of number classification, quick recall of divisibility rules, and confident handling of negative integers. These skills appear repeatedly across the mathematics section.

Key Concepts

• **Natural Numbers**: Counting numbers starting from 1 (i.e., 1, 2, 3, 4, ...). Zero is not a natural number.

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

• **Integers**: Whole numbers plus their negatives (..., -3, -2, -1, 0, 1, 2, 3, ...). Integers include positive numbers, negative numbers, and zero.

• **Place Value vs Face Value**: Place value depends on the position of a digit (e.g., 5 in 3527 has place value 500), while face value is the digit itself (face value of 5 is always 5).

• **Factors**: Numbers that divide a given number exactly without leaving a remainder. Every number has at least two factors: 1 and itself.

• **Multiples**: Numbers obtained by multiplying a given number by natural numbers. A number has infinitely many multiples.

• **Prime Numbers**: Numbers greater than 1 with exactly two factors (1 and the number itself). Examples: 2, 3, 5, 7, 11, 13.

• **Composite Numbers**: Numbers greater than 1 with more than two factors. The number 1 is neither prime nor composite.

Formulas / Key Facts

| Concept | Key Fact | |---------|----------| | Smallest natural number | 1 | | Smallest whole number | 0 | | Smallest prime number | 2 (also the only even prime) | | Number of factors of a prime | Exactly 2 | | 1 is | Neither prime nor composite | | Place value of digit d at position p | d × 10^(p-1), counting from right starting at position 1 | | Sum of first n natural numbers | n(n+1)/2 | | Product of two numbers | LCM × HCF |

**Divisibility Rules (must memorize):**