Number System
About 6 min · Quantitative Ability · English
Time worked out from the lesson's 370 words at 150 words a minute, plus a minute for each question.
The Number System forms the bedrock of Quantitative Ability in HSSC CET. Nearly every arithmetic topic—from simplification to data interpretation—relies on your fluency with numbers, their types, and their properties.
Key ideas
- Natural Numbers (N): Counting numbers starting from 1. Example: 1, 2, 3, 4, ...
- Whole Numbers (W): Natural numbers plus zero. Example: 0, 1, 2, 3, ...
- Integers (Z): All whole numbers and their negatives. Example: ..., −3, −2, −1, 0, 1, 2, 3, ...
- Rational Numbers: Numbers expressible as p/q where p, q are integers and q ≠ 0. Every terminating or repeating decimal is rational.
- Place Value vs Face Value: In 5832, the face value of 8 is simply 8, but the place value of 8 is 800 (8 × 100).
Watch out for
- Confusing place value with face value → Remember: place value depends on position (hundreds, thousands, etc.), face value is just the digit itself. In 4052, place value of 5 is 50, not 5.
- Forgetting that 1 is not prime → Prime numbers must have exactly two distinct factors. The number 1 has only one factor (itself), so it is neither prime nor composite.
- Applying the wrong divisibility rule for 4 vs 8 → For 4, check last two digits. For 8, check last three digits. Students often mix these up under pressure.
Quick reference
- Divisibility by 6 = divisible by BOTH 2 and 3.
- Sum of digits trick: quickly add digits to test divisibility by 3 or 9.
- Unit digit cycles: 2, 3, 7, 8 repeat every 4 powers; 4, 9 repeat every 2 powers.
- Factors formula: N = a^p × b^q (a, b distinct primes) → Total factors = (p+1)(q+1).
- First 10 primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 (only even prime is 2).
Check yourself: 3 questions
1. The sum of the digits of a two-digit number is 9. If 27 is added to the number, the digits get reversed. What is the original number?
2. How many natural numbers less than 500 are divisible by both 6 and 8?
3. A number when divided by 7 leaves a remainder of 4. What will be the remainder when the square of the same number is divided by 7?
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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