07. Divisibility Rules (2–12, 15, 16, 18, etc.)
Divisibility rules ka complete chart: 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,25; SSC CGL tricks + examples + practice questions with answers.
1) Divisibility ka matlab (very simple)
Agar kisi number ko kisi divisor se divide karne par remainder 0 aaye,
to number us divisor se divisible hai.
Example: 84 ÷ 7 = 12 (remainder 0) ⇒ 84 is divisible by 7.
2) Most used divisibility rules (SSC CGL)
| Divisor |
Rule (quick test) |
Example |
| 2 |
Last digit even (0,2,4,6,8) |
124 (✓), 135 (✗) |
| 3 |
Digits ka sum 3 se divisible |
462 (4+6+2=12 ✓) |
| 4 |
Last 2 digits 4 se divisible |
1316 → 16 ✓ |
| 5 |
Last digit 0 ya 5 |
930 (✓), 927 (✗) |
| 6 |
2 aur 3 dono se divisible (even + sum divisible by 3) |
198 (even, 1+9+8=18 ✓) |
| 8 |
Last 3 digits 8 se divisible |
1760 → 760 ÷ 8 = 95 ✓ |
| 9 |
Digits ka sum 9 se divisible |
729 (7+2+9=18 ✓) |
| 10 |
Last digit 0 |
540 (✓) |
| 11 |
(Odd place sum − Even place sum) = 0 ya 11 ka multiple |
121: (1+1)−2=0 ✓ |
| 12 |
3 aur 4 dono se divisible |
372 (sum 12 ✓, last2 72 ✓) |
3) Extra useful rules (SSC me aate hain)
Divisible by 15
- 3 aur 5 dono se divisible
- Example: 345 (sum 12 ⇒ 3 se divisible; last digit 5 ⇒ 5 se divisible) ⇒ 15 se divisible
Divisible by 16
- Last 4 digits 16 se divisible
- Example: 123456 → last4 = 3456; 3456 ÷ 16 = 216 ⇒ divisible
Divisible by 18
- 2 aur 9 dono se divisible
- Example: 774 (even; sum 7+7+4=18 ⇒ 9 se divisible) ⇒ 18 se divisible
Divisible by 20
- Last two digits divisible by 20 (or number divisible by 4 and last digit 0)
- Example: 1540 (last2 = 40 ✓) ⇒ divisible
Divisible by 25
- Last two digits: 00, 25, 50, 75
- Example: 9875 (✓), 9800 (✓)
4) Divisibility by 7 (simple SSC trick)
7 ka rule multiple methods me aata hai. SSC ke liye safe/fast:
Direct division ya last 3 digits check with known multiples.
- Multiples of 7 near 1000: 994, 1001, 1008...
- Example: 2030 divisible by 7? 2030 = 1960 + 70 ⇒ 7×280 + 7×10 ⇒ divisible
Note: 7/13 ke complex digit rules exist, but SSC me usually 2–12/15/16/18/25/11 dominate. 7 ke liye mental division/approx multiples best.
5) Common traps
- 4 ka rule last 2 digits; 8 ka rule last 3 digits; 16 ka rule last 4 digits.
- 6 ka rule: “even” alone enough nahi, digits sum bhi 3 se divisible hona chahiye.
- 11 ka rule me alternating sums ka difference 11 ka multiple hona chahiye (negative bhi allowed).
6) Practice (SSC CGL) + Answers
- Check: 7424 divisible by 4 and 8?
- Which are divisible by 9: 513, 999, 1008?
- Is 462 divisible by 6?
- Check 1232 divisible by 16?
- Which are divisible by 25: 2450, 3175, 8906, 1200
- Using 11 rule: 91827 divisible by 11?
Show Answers
- 4: last2=24 ✓; 8: last3=424 (424÷8=53) ✓
- 513 (5+1+3=9 ✓), 999 (27 ✓), 1008 (9 ✓) ⇒ all three divisible by 9
- 462 even ✓ and sum=4+6+2=12 (3 se divisible ✓) ⇒ 6 se divisible
- Last4=1232; 1232÷16=77 ✓
- 2450 (50 ✓), 3175 (75 ✓), 8906 (✗), 1200 (00 ✓)
- Odd places: 9+8+7=24; Even places: 1+2+2=5; diff=19 (11 multiple nahi) ⇒ not divisible
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