SSC Notes / Quantitative Aptitude / Chapter 1
Chapter 1 of 27

Number System

Types of numbers, place value, unit digit tricks, and remainder theorems — the foundation every other SSC Quant chapter builds on.

📖 ~13 min read 🔢 SSC Quantitative Aptitude

Introduction

Number System is the base chapter for the entire SSC Quant section — questions from HCF-LCM, divisibility, simplification, and even Data Interpretation all lean on the concepts covered here. Master this chapter first.

Types of Numbers

TypeDefinitionExample
Natural Numbers (N)Counting numbers starting from 11, 2, 3, 4...
Whole Numbers (W)Natural numbers + 00, 1, 2, 3...
Integers (Z)Whole numbers + negative numbers...-2, -1, 0, 1, 2...
Rational NumbersCan be expressed as p/q, q≠01/2, 0.75, 5
Irrational NumbersCannot be expressed as p/q; non-terminating, non-repeating decimals√2, π
Prime NumbersExactly two factors — 1 and itself2, 3, 5, 7, 11, 13...
Composite NumbersMore than two factors4, 6, 8, 9, 10...
⚠️ Common Trap: 1 is neither prime nor composite. 2 is the only even prime number — SSC loves testing this directly.

Unit Digit Trick

To find the unit digit of a^b, find the cyclicity of the unit digit of the base "a," then use (b mod cycle length) to pick the right digit from the cycle.

Last Digit of BaseCyclicityPattern
0, 1, 5, 61Always same digit
4, 92e.g., 4 → 4,6,4,6...
2, 3, 7, 84e.g., 2 → 2,4,8,6,2,4,8,6...
Q. Find the unit digit of 47^63.
Unit digit of base = 7 → cyclicity 4 pattern: 7,9,3,1
63 ÷ 4 → remainder 3 → 3rd term in the cycle = 3

Remainder Theorem Basics

  • (a × b) mod n = [(a mod n) × (b mod n)] mod n — remainders can be multiplied and reduced at each step, avoiding large calculations.
  • (a + b) mod n = [(a mod n) + (b mod n)] mod n — same principle applies to addition.
Q. Find the remainder when 15 × 17 × 19 is divided by 7.
15 mod 7 = 1, 17 mod 7 = 3, 19 mod 7 = 5
(1 × 3 × 5) mod 7 = 15 mod 7 = 1

Divisibility Basics (Full rules in next chapters)

A number is divisible by another if the remainder on division is 0. This concept is central to HCF/LCM (Chapter 3) and gets a full dedicated ruleset in Chapter 4.

Face Value vs Place Value

TermMeaningExample (digit 5 in 4532)
Face ValueThe digit itself5
Place ValueDigit × value of its position5 × 100 = 500
💡 Exam Tip: For unit digit and remainder-based questions, never calculate the full large power/product — always reduce using cyclicity or the remainder theorem first. This is the single biggest time-saver in this chapter.
✅ Practice Focus: Unit digit of large powers · Remainder of products/sums using modular reduction · Prime vs composite classification · Face value vs place value distinction.

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