Number System
Number System
Number System tests divisibility, HCF, LCM, remainders, and prime factorization. SSC and RRB papers repeat HCF/LCM and remainder problems almost every session. Trailing-zeros-in-factorial is a guaranteed one-mark question in SSC CGL Tier 1. Build speed on factor counting and cyclicity \u2014 these two skills unlock the hardest variants.
Key Idea
HCF × LCM = Product of two numbers (valid for exactly two numbers only). Always verify divisibility before computing HCF/LCM.
Core Formulas
HCF × LCM Relationship
HCF(a, b) × LCM(a, b) = a × b
Compute one value from the other instantly \u2014 if the exam gives HCF and the product of two numbers, divide to get LCM (or vice versa).
Number of Factors
If n = p₁^a × p₂^b × p₃^c, factors = (a+1)(b+1)(c+1)
Prime-factorise the number first, then multiply incremented exponents \u2014 this counts all divisors including 1 and the number itself.
Trailing Zeros in n!
Zeros = ⌊n/5⌋ + ⌊n/25⌋ + ⌊n/125⌋ + …
To find how many trailing zeros appear in the factorial of a large number.
Sum of First n Natural Numbers
Sₙ = n(n+1)/2
For sum of 1+2+3+…+n; extend to squares: n(n+1)(2n+1)/6; cubes: [n(n+1)/2]²
Remainder of Large Powers
aⁿ mod m — find cycle: a¹, a², a³ mod m; use n mod (cycle length) to pick remainder
When asked for remainder of 2^100 ÷ 7 or similar large-power division problems.
Relevant Exams
Number System questions appear in almost every SSC and RRB exam — HCF/LCM and remainder problems are among the most frequently repeated topics.