The Number System forms the bedrock of elementary mathematics and appears consistently in HP TET Mathematics. This topic tests your understanding of how numbers are structured, classified, and manipulated—skills essential for teaching primary students who are encountering formal mathematics for the first time.
For HP TET, expect questions on identifying number types, place value problems, divisibility rules, and finding factors/multiples. The pedagogy section may also ask how to introduce these concepts to young learners. Mastering this topic is non-negotiable because it underpins fractions, decimals, algebra, and virtually every other mathematics topic in the syllabus.
You must be fluent with: classifying numbers correctly, expanding numbers using place value, applying divisibility tests quickly, and finding HCF/LCM through factors. Speed and accuracy matter—these are typically straightforward questions where you cannot afford errors.
Key Concepts
**Natural Numbers (N)**: Counting numbers starting from 1. Set = {1, 2, 3, 4, ...}. Zero is NOT a natural number.
**Whole Numbers (W)**: Natural numbers plus zero. Set = {0, 1, 2, 3, ...}. Every natural number is a whole number, but 0 is whole and not natural.
**Integers (Z)**: Whole numbers plus negative counterparts. Set = {..., -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 (never changes). Place value = digit × position value. In 4827, the face value of 8 is 8, but place value of 8 is 800.
**Factors**: Numbers that divide a given number exactly (remainder = 0). Every number has 1 and itself as factors. Factors are always ≤ the number.
**Multiples**: Numbers obtained by multiplying a given number by natural numbers. Multiples are always ≥ the number. A number has infinite multiples but finite factors.
**Prime Numbers**: Numbers with exactly two factors (1 and itself). Examples: 2, 3, 5, 7, 11, 13... Note: 1 is NOT prime (only one factor). 2 is the only even prime.
**Composite Numbers**: Numbers with more than two factors. Examples: 4, 6, 8, 9, 10... Note: 1 is neither prime nor composite.
Formulas / Key Facts
**Place Value System (Indian)**
Ones, Tens, Hundreds, Thousands, Ten Thousands, Lakhs, Ten Lakhs, Crores
1 Lakh = 1,00,000; 1 Crore = 1,00,00,000
**Divisibility Rules**
Need more? Ask Shishya
Shishya is your personal tutor for this topic. Pick a starter or open a free chat.
**Mistake 1: Including 0 in natural numbers** Wrong thinking: "Natural numbers are 0, 1, 2, 3..." Correct fix: Natural numbers start from 1. Zero is a whole number but NOT a natural number.
**Mistake 2: Confusing factors and multiples** Wrong thinking: "Factors of 6 are 6, 12, 18..." or "Multiples of 6 are 1, 2, 3, 6" Correct fix: Factors divide INTO the number (≤ the number). Multiples are obtained BY multiplying (≥ the number).
**Mistake 3: Calling 1 a prime number** Wrong thinking: "1 has only 1 and itself as factors, so it's prime" Correct fix: Prime numbers have exactly TWO distinct factors. 1 has only ONE factor (itself), so it is neither prime nor composite.
**Mistake 4: Applying divisibility by 4 incorrectly** Wrong thinking: Checking if sum of digits is divisible by 4 Correct fix: For divisibility by 4, check only the last TWO digits. For 724: check 24 ÷ 4 = 6 (yes).
**Mistake 5: Forgetting that 2 is prime and even** Wrong thinking: "All prime numbers are odd" Correct fix: 2 is the only even prime number. It has exactly two factors: 1 and 2.
Quick Reference
Natural: starts at 1 | Whole: starts at 0 | Integers: include negatives
Place value = Face value × Position value
1 is neither prime nor composite; 2 is the only even prime
Divisibility by 3 and 9: use sum of digits
Divisibility by 4: last two digits; by 8: last three digits
Factors are finite and ≤ N; Multiples are infinite and ≥ N