Divisibility Rules
SSC GD Exam - Quantitative Aptitude
1. Introduction to Divisibility Rules
Divisibility rules help us determine whether a given number is divisible by another number without performing full division. These shortcuts are useful for finding factors, LCM, HCF, and for simplifying arithmetic problems quickly.
Key Benefit:
Save time in competitive exams by quickly identifying factors and multiples without lengthy
calculations.
2. Basic Divisibility Rules
| Number | Divisibility Rule | Example |
|---|---|---|
| 2 | Last digit is even (0, 2, 4, 6, 8) | 128 → ✅ (ends with 8) |
| 3 | Sum of digits is divisible by 3 | 258 → 2+5+8=15 → ✅ |
| 4 | Last two digits form a number divisible by 4 | 312 → 12 ÷ 4 = 3 → ✅ |
| 5 | Last digit is 0 or 5 | 465 → ✅ (ends with 5) |
| 6 | Divisible by both 2 and 3 | 132 → even and 1+3+2=6 → ✅ |
| 8 | Last three digits form a number divisible by 8 | 3128 → 128 ÷ 8 = 16 → ✅ |
| 9 | Sum of digits is divisible by 9 | 837 → 8+3+7=18 → ✅ |
| 10 | Last digit is 0 | 450 → ✅ |
| 11 | Difference between sum of alternate digits is 0 or divisible by 11 | 506 → (5+6)–0=11 → ✅ |
| 12 | Divisible by both 3 and 4 | 324 → 3+2+4=9 & 24÷4=6 → ✅ |
| 15 | Divisible by both 3 and 5 | 345 → ✅ |
| 25 | Last two digits form a number divisible by 25 | 825 → ✅ (25×33) |
| 50 | Last two digits are 00 or 50 | 450 → ✅ |
| 100 | Last two digits are 00 | 700 → ✅ |
3. Special Divisibility Rules
Rule for 7
Double the last digit and subtract from the remaining number.
Example: 462 → 46 - (2×2) = 42 → divisible by 7 ✅
Rule for 11
(Sum of odd-place digits) - (Sum of even-place digits) = 0 or multiple of 11
Example: 121 → (1+1) - 2 = 0 → divisible by 11 ✅
Rule for 13
Multiply last digit by 4 and add to remaining number.
Example: 169 → 16 + (9×4) = 52 → divisible by 13 ✅
Composite Numbers
For composite numbers, check divisibility by their prime factors
Example: 18 = 2×3×3 → check divisibility by 2 and 9
4. Memory Tips & Tricks
Last Digit Rules: 2, 5, 10 - check only last digit
Sum Rules: 3, 9 - check sum of all digits
Last 2/3 Digits: 4, 8, 25, 50, 100 - check last few digits
Combination Rules: 6, 12, 15 - check multiple conditions
Quick Reference Pattern
2, 5, 10
Last digit only
3, 9
Sum of digits
4, 8, 25
Last 2-3 digits
6, 12, 15
Multiple rules
5. Exam Application Tips
Quick Factor Identification
Use divisibility rules to quickly identify factors in LCM/HCF problems
Number System Questions
Essential for questions about multiples, factors, and prime numbers
Simplification
Simplify fractions quickly by identifying common factors
Time Saving
Save 30-60 seconds per question by avoiding long division
6. Quick Recap - Most Important Rules
| Number | Rule | Priority |
|---|---|---|
| 2, 5, 10 | Check last digit | High |
| 3, 9 | Sum of digits | High |
| 4, 8, 25 | Last 2-3 digits | Medium |
| 6, 12, 15 | Multiple conditions | Medium |
| 7, 11, 13 | Special rules | Low |
7. Practice Questions
Test your knowledge with these practice questions. Click on "View Answer" to check your understanding.
Q1. Is 246 divisible by 2?
View Answer
Yes, last digit is 6 (even).
Q2. Is 375 divisible by 5?
View Answer
Yes, ends with 5.
Q3. Check if 216 is divisible by 3.
View Answer
Sum = 2+1+6=9 → divisible by 3 ✅
Q4. Check if 924 is divisible by 4.
View Answer
Last two digits 24 → 24 ÷ 4 = 6 → ✅
Q5. Is 450 divisible by 6?
View Answer
Divisible by 2 (even) and 3 (4+5+0=9) → ✅
Q6. Check if 1032 is divisible by 8.
View Answer
Last 3 digits 032 → 32 ÷ 8 = 4 → ✅
Q7. Is 639 divisible by 9?
View Answer
Sum = 6+3+9=18 → divisible by 9 ✅
Q8. Check if 121 is divisible by 11.
View Answer
(1+1)–2=0 → divisible by 11 ✅
Q9. Is 500 divisible by 25?
View Answer
Last two digits 00 → ✅
Q10. Is 1250 divisible by 50?
View Answer
Last two digits 50 → ✅
Q11. Check divisibility of 360 by 12.
View Answer
Divisible by 3 (3+6+0=9) and 4 (60 ÷ 4 = 15) → ✅
Q12. Check if 105 is divisible by 15.
View Answer
Divisible by 3 (sum=6) and 5 (ends in 5) → ✅
Q13. Is 273 divisible by 3?
View Answer
Sum=2+7+3=12 → ✅
Q14. Is 462 divisible by 7?
View Answer
46 – 2×2 = 42 → 42 ÷ 7 = 6 → ✅
Q15. Which of the following numbers is divisible by 9: 1458, 1234, 5673?
View Answer
1458 (sum=18 → ✅), 1234 (sum=10 ❌), 5673 (sum=21 → ✅)
✅ Exam Strategy Tip
🟢 Start with 2, 5, 10 rules first - they're the quickest to check
🟢 For composite numbers, check divisibility by prime factors
🟢 Practice mental calculation of digit sums for 3 and 9
🟢 Remember patterns: 4/8/25 check last digits, 6/12/15 check combinations
You've completed Divisibility Rules Concepts!
Courage Tip: Regular practice with divisibility rules will significantly improve your speed in number system questions. Focus on mastering the most frequently tested rules (2, 3, 5, 9, 10, 11) first, then move to less common ones. Create flashcards for quick revision and practice applying these rules in LCM/HCF problems to build comprehensive understanding.
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