SSC CGL Math Number System: Chapter 1: Number System & Divisibility Rules – मज़ेदार मैथ्स की शुरुआत
🔢 1.1 Types of Numbers – Know Your Numbers
| Number Type | Definition | Example |
|---|---|---|
| Natural Numbers | Counting numbers | 1, 2, 3, 4… |
| Whole Numbers | Natural numbers + 0 | 0, 1, 2, 3… |
| Integers | Negative + Zero + Positive numbers | -3, 0, 5 |
| Rational Numbers | Numbers expressed as p/q | 3/4, -2/5 |
| Irrational Numbers | Can’t be expressed as p/q | √2, π |
| Prime Numbers | Only divisible by 1 & itself | 2, 3, 5, 7 |
| Composite Numbers | More than 2 factors | 4, 6, 8, 9 |
🔄 1.2 Even-Odd Concepts & Examples
✨ Rules:
Even + Even = Even
Odd + Odd = Even
Even + Odd = Odd
Odd × Odd = Odd
Even × Even = Even
Even × Odd = Even
💡 Example:
Q: What is the result of 24 + 37?
→ Even + Odd = Odd
Q: What is the product of 9 × 5?
→ Odd × Odd = Odd
Shortcut Tip:
If your answer must be odd, all numbers multiplied must be odd.
🎯 1.3 Divisibility Rules with Examples
| Divisible By | Rule | Example |
|---|---|---|
| 2 | Last digit even | 346 → Yes |
| 3 | Sum of digits divisible by 3 | 2+4+1 = 7 → No |
| 4 | Last 2 digits divisible by 4 | 512 → 12 ÷ 4 = 3 ✅ |
| 5 | Ends in 0 or 5 | 465 → Yes |
| 6 | Div by 2 AND 3 | 246 → Even & 2+4+6=12 ✔ |
| 7 | Double last digit, subtract | 203 → 20 – 6 = 14 → Yes |
| 8 | Last 3 digits ÷ 8 | 7120 → 120 ÷ 8 = 15 ✔ |
| 9 | Digit sum divisible by 9 | 7+2+9 = 18 → ✔ |
| 10 | Ends in 0 | 570 → ✔ |
| 11 | Alt sum-diff divisible by 11 | 2728 → 2-7+2-8 = -11 → ✔ |
🧠 1.4 Digital Root (Single Digit Sum)
Trick: Keep adding digits until a single digit remains.
💡 Example:
Q: What is the digital root of 5432?
→ 5 + 4 + 3 + 2 = 14 → 1 + 4 = 5
✨ SSC Tip:
Use it to eliminate MCQ options fast!
🔢 1.5 Unit Digit of Big Powers
🔍 Concept:
Every number’s unit digit repeats in a cycle.
💡 Example:
Q: Unit digit of 7¹⁰⁰?
Cycle of 7 = 7, 9, 3, 1 (length 4)
100 ÷ 4 = Remainder 0 → Take 4th digit in cycle = 1
Q: Unit digit of 2³⁵?
Cycle of 2 = 2, 4, 8, 6 → 35 ÷ 4 = R3 → 3rd = 8
📌 1.6 Highest Power of Prime in Factorial
Formula:
Power of p in n! = n/p + n/p² + n/p³ + …
💡 Example:
Q: Highest power of 2 in 50!
→ 50/2 + 50/4 + 50/8 + 50/16 + 50/32
= 25 + 12 + 6 + 3 + 1 = 47
🎉 1.7 Fun Fact – Count of Zeros in Factorials
Trick:
Zeros = Number of 5s in factors
💡 Example:
Q: How many zeros in 100!?
→ 100/5 + 100/25 + 100/125 = 20 + 4 + 0 = 24
📊 1.8 Shortcut Box Recap
| Concept | Shortcut |
|---|---|
| Divisible by 3 | Sum of digits |
| Unit digit | Use power cycles |
| Digital root | Sum till single digit |
| Zeros in n! | n/5 + n/25 + … |
| Highest power of p in n! | n/p + n/p² + … |
🧪 Practice Set: Chapter 1 – Concept Based (With Examples)
📝 Solve with tricks. Try under 10 minutes!
What is the unit digit of 9²³?
Find the digital root of 87654321
How many zeros are in 125!?
Which number is divisible by 11: 121, 1221, 1331?
Find highest power of 3 in 100!
Is 348 divisible by 3?
Is 278 divisible by 4?
Which number has unit digit 2: 2³, 2⁵, 2⁷?
Find the LCM of 12 and 18
Find the HCF of 36 and 60
✅ Answer Key with Explanation
| Q | Ans | Explanation |
|---|---|---|
| 1 | 9 | 9^odd always ends in 9 |
| 2 | 9 | Sum = 36 → 3+6 = 9 |
| 3 | 31 | 125/5 + 125/25 + 125/125 = 25+5+1 |
| 4 | 1331 | Alt sum = 1–3+3–1 = 0 ✔ |
| 5 | 48 | 100/3 + 100/9 + 100/27 + 100/81 = 33+11+3+1 |
| 6 | Yes | 3+4+8 = 15 → div by 3 ✔ |
| 7 | No | Last 2 digits = 78 → 78 ÷ 4 = 19.5 ❌ |
| 8 | 2⁵ = 32 | Unit digit = 2 |
| 9 | 36 | LCM(12,18) = (12×18)/HCF = 216/6 |
| 10 | 12 | HCF(36,60) = 12 |
