Number System — SSC CHSL Study Notes
Overview
The Number System forms the backbone of Quantitative Aptitude in SSC CHSL. Expect 3–5 direct questions from this topic in Tier 1, plus countless indirect applications across other arithmetic topics. Mastery here speeds up your entire math section.
This topic tests your understanding of how numbers behave: divisibility patterns, prime factorization, finding HCF and LCM, working with fractions and decimals, and simplifying surds. SSC loves testing these concepts through word problems, formula applications, and quick mental math scenarios. Students who internalize divisibility rules and master fraction–decimal conversions save 20–30 seconds per question elsewhere in the paper.
Focus on pattern recognition rather than lengthy calculations. Many CHSL questions reward spotting shortcuts — like recognizing that a number divisible by both 3 and 4 must be divisible by 12, or converting recurring decimals to fractions instantly.
Key Concepts
• **Natural, Whole, and Integers**: Natural numbers (1, 2, 3…), whole numbers (0, 1, 2…), integers (…−2, −1, 0, 1, 2…). Know the difference; questions often test which set a result belongs to.
• **Prime and Composite Numbers**: A prime has exactly two factors (1 and itself); 2 is the only even prime. Composite numbers have more than two factors. 1 is neither prime nor composite.
• **Divisibility Rules**: Quick mental checks — divisibility by 2 (last digit even), by 3 (sum of digits divisible by 3), by 4 (last two digits divisible by 4), by 5 (ends in 0 or 5), by 6 (divisible by both 2 and 3), by 8 (last three digits divisible by 8), by 9 (sum of digits divisible by 9), by 11 (difference of alternate digit sums divisible by 11).
• **HCF and LCM**: HCF (Highest Common Factor) is the largest number dividing all given numbers. LCM (Lowest Common Multiple) is the smallest number all given numbers divide into. For two numbers a and b: **HCF × LCM = a × b**.
• **Fractions**: Proper fraction (numerator < denominator), improper fraction (numerator ≥ denominator), mixed number (whole + proper fraction). Convert between forms fluently.
• **Decimals**: Terminating decimals end (0.25), non-terminating repeating decimals recur (0.333…). Any fraction with denominator having only 2s and 5s as prime factors terminates; otherwise it recurs.
• **Surds**: Irrational roots like √2, √3, ∛5. Rationalization means removing surds from denominators by multiplying by the conjugate (e.g., multiply 1/√2 by √2/√2 to get √2/2).
• **Co-primes**: Two numbers are co-prime if their HCF is 1 (e.g., 8 and 15). Co-primes need not be prime themselves.
Formulas / Key Facts
• **Product formula**: For any two numbers a and b, **a × b = HCF(a,b) × LCM(a,b)**
• **LCM of fractions** = LCM of numerators / HCF of denominators
• **HCF of fractions** = HCF of numerators / LCM of denominators