RRB Group D · Bite-size lessons
Number System
About 6 min · Mathematics · English
Time worked out from the lesson's 323 words at 150 words a minute, plus a minute for each question.
The Number System is the foundation of all quantitative reasoning in Railway Group D exams. Mastery here means you can classify any number instantly, apply divisibility tests without scratch work, and recognize properties like prime factorization reflexively.
Key ideas
- Natural Numbers (N): Counting numbers starting from 1: {1, 2, 3, 4, ...}. Used for counting discrete objects; no zero, negatives, or fractions.
- Whole Numbers (W): Natural numbers plus zero: {0, 1, 2, 3, ...}. Zero represents "nothing" and is the additive identity.
- Integers (Z): All whole numbers plus their negatives: {..., -3, -2, -1, 0, 1, 2, 3, ...}. Closed under addition, subtraction and multiplication but not division.
- Rational Numbers (Q): Any number expressible as p/q where p and q are integers and q ≠ 0. Includes terminating decimals (0.75 = 3/4) and repeating decimals (0.333... = 1/3). All integers are rational since 5 = 5/1.
- Prime Numbers: Natural numbers greater than 1 with exactly two factors: 1 and itself. First ten primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. Note: 2 is the only even prime; 1 is neither prime nor composite.
Quick reference
- Number hierarchy: Natural ⊂ Whole ⊂ Integer ⊂ Rational.
- Divisibility shortcuts: 3 (digit sum), 4 (last two), 8 (last three), 9 (digit sum), 11 (alternating digit sum).
- 2 is the only even prime; 1 is neither prime nor composite.
- Co-prime: HCF = 1, not necessarily prime themselves.
- Sum formulas: First n naturals = n(n+1)/2; first n odds = n².
Check yourself: 3 questions
1. A number when divided by 5 leaves a remainder of 3. If the same number is divided by 15, what can be the possible remainder?
2. What is the smallest natural number that is divisible by both 8 and 12?
3. If a number is divisible by both 3 and 4, which of the following numbers must also divide it?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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