Number System
About 5 min · Mathematics · English
Time worked out from the lesson's 289 words at 150 words a minute, plus a minute for each question.
The Number System is the foundation of mathematics and part of the RRB NTPC Mathematics syllabus. Mastery here builds confidence for the entire Math section.
Key ideas
- Natural Numbers (N): Counting numbers starting from 1: {1, 2, 3, 4, ...}. Used when counting discrete objects. Zero is not a natural number.
- Whole Numbers (W): Natural numbers plus zero: {0, 1, 2, 3, ...}. Represents quantities that can be zero (e.g., items in an empty basket).
- Integers (Z): All positive and negative whole numbers including zero: {..., -3, -2, -1, 0, 1, 2, 3, ...}. No fractions or decimals.
- Rational Numbers (Q): Any number expressible as p/q where p and q are integers and q ≠ 0. Includes terminating decimals (0.5 = 1/2) and repeating decimals (0.333... = 1/3). Every integer is rational (5 = 5/1).
- Divisibility: A number a is divisible by b if a ÷ b leaves no remainder. Divisibility tests help you check this mentally without performing full division.
Quick reference
- Natural: {1,2,3,...}; Whole: {0,1,2,...}; Integers: {...,-1,0,1,...}; Rationals: p/q form.
- Divisibility by 3 → sum of digits divisible by 3; by 9 → sum divisible by 9.
- Divisibility by 4 → last 2 digits; by 8 → last 3 digits.
- Number of factors of p₁^a × p₂^b = (a+1)(b+1).
- HCF = product of lowest powers of common primes; LCM = product of highest powers.
Check yourself: 3 questions
1. A number when divided by 296 leaves a remainder of 75. What will be the remainder when the same number is divided by 37?
2. Find the largest 4-digit number which is exactly divisible by 88.
3. The sum of two numbers is 528 and their HCF is 33. How many pairs of such numbers can exist?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 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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