Divisibility Rules for SSC CGL - Complete Guide | Test of Divisibility 2 to 11 in in Hinglish (Hindi +English)

📌 Series Info: Ye post Chapter 1: Number System ka part hai.
Post Number: 2/76 | Topic: 1.2 Divisibility Rules (2 to 11)

Introduction: Divisibility Rules Kyu Important Hain?

Namaste dosto! Aaj ham Divisibility Rules (विभाज्यता के नियम) padhenge. Ye SSC CGL, OSSC CGL, Bank, Railway jaise sabhi government exams me bahut important topic hai.

Divisibility Rules ka matlab hai: Bina actual division kiye pata lagana ki koi number kisi aur number se completely divide hota hai ya nahi (remainder 0 aaye).

🎯 Exam Importance: Number System, HCF-LCM, Prime Factorization, aur Speed Calculation ke liye ye rules must hain. Direct 2-3 questions + indirect bahut questions me use hote hain.

Kya Sikhenge Is Post Me?

Divisibility Rules for 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
Har rule ke examples with step-by-step solution
Memory tricks aur shortcuts
SSC CGL level practice questions

1. Divisibility Rule for 2

🔹 Rule: Agar number ka last digit (unit digit) even hai (0, 2, 4, 6, 8), toh wo number 2 se divisible hai.

Examples:

Example 1: Kya 248 divisible by 2 hai?
Solution: Last digit = 8 (even) → ✓ Divisible by 2

Example 2: Kya 357 divisible by 2 hai?
Solution: Last digit = 7 (odd) → ✗ Not divisible by 2

✓ 10, 22, 34, 56, 100, 2468 (sab 2 se divisible)
✗ 11, 23, 35, 47, 999 (2 se divisible nahi)

💡 Quick Trick: Sirf last digit dekho. Even = Divisible, Odd = Not divisible

2. Divisibility Rule for 3

🔹 Rule: Agar number ke sabhi digits ka sum 3 se divisible hai, toh wo number bhi 3 se divisible hai.

Examples:

Example 1: Kya 123 divisible by 3 hai?
Solution:
Sum of digits = 1 + 2 + 3 = 6
6 ÷ 3 = 2 (divisible) → ✓ 123 is divisible by 3

Example 2: Kya 2584 divisible by 3 hai?
Solution:
Sum = 2 + 5 + 8 + 4 = 19
19 ÷ 3 = 6.33 (not divisible) → ✗ Not divisible by 3

✓ 15 (1+5=6), 27 (2+7=9), 111 (1+1+1=3), 9999 (9+9+9+9=36)
✗ 25 (2+5=7), 100 (1+0+0=1)

💡 Pro Trick: Agar sum bada ho, toh dubara us sum ke digits ka sum nikalo.
Example: 5832 → 5+8+3+2 = 18 → 1+8 = 9 → Divisible by 3 ✓

3. Divisibility Rule for 4

🔹 Rule: Agar number ke last 2 digits 4 se divisible hain (ya 00 hain), toh wo number 4 se divisible hai.

Examples:

Example 1: Kya 1328 divisible by 4 hai?
Solution:
Last 2 digits = 28
28 ÷ 4 = 7 → ✓ Divisible by 4

Example 2: Kya 2546 divisible by 4 hai?
Solution:
Last 2 digits = 46
46 ÷ 4 = 11.5 (not divisible) → ✗ Not divisible by 4

✓ 116 (16÷4=4), 2500 (00), 9316 (16÷4=4)
✗ 235 (35÷4=8.75), 1111 (11÷4=2.75)

💡 Memory Trick: Last 2 digits yaad kar lo jo 4 se divisible hote hain:
00, 04, 08, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96

4. Divisibility Rule for 5

🔹 Rule: Agar number ka last digit 0 ya 5 hai, toh wo number 5 se divisible hai.

Examples:

Example 1: Kya 125 divisible by 5 hai?
Solution: Last digit = 5 → ✓ Divisible by 5

Example 2: Kya 238 divisible by 5 hai?
Solution: Last digit = 8 → ✗ Not divisible by 5

✓ 10, 25, 35, 100, 1005, 99995
✗ 12, 33, 47, 1002, 9998

💡 Sabse Easy Rule: Sirf 0 ya 5 last me ho → Divisible!

5. Divisibility Rule for 6

🔹 Rule: Agar number 2 se bhi divisible hai aur 3 se bhi divisible hai, toh wo 6 se divisible hai.

Examples:

Example 1: Kya 132 divisible by 6 hai?
Solution:
• Check for 2: Last digit = 2 (even) → Divisible by 2 ✓
• Check for 3: 1+3+2 = 6 (divisible by 3) → Divisible by 3 ✓
Result: ✓ 132 divisible by 6

Example 2: Kya 124 divisible by 6 hai?
Solution:
• Check for 2: Last digit = 4 (even) → Divisible by 2 ✓
• Check for 3: 1+2+4 = 7 (not divisible by 3) → Not divisible by 3 ✗
Result: ✗ Not divisible by 6

✓ 18, 24, 36, 102, 252, 1008
✗ 15 (3 se hai, 2 se nahi), 20 (2 se hai, 3 se nahi)

💡 Shortcut: Divisibility by 6 = Divisibility by 2 AND 3 dono check karo

6. Divisibility Rule for 7 IMPORTANT

🔹 Rule: Last digit ko 2 se multiply karo aur baaki number se subtract karo. Agar result 7 se divisible hai (ya 0 hai), toh original number bhi 7 se divisible hai.

Examples:

Example 1: Kya 203 divisible by 7 hai?
Solution:
• Last digit = 3, Baaki part = 20
• 3 × 2 = 6
• 20 - 6 = 14
• 14 ÷ 7 = 2 → ✓ 203 divisible by 7

Example 2: Kya 154 divisible by 7 hai?
Solution:
• Last digit = 4, Baaki = 15
• 4 × 2 = 8
• 15 - 8 = 7
• 7 ÷ 7 = 1 → ✓ 154 divisible by 7

Example 3: Kya 123 divisible by 7 hai?
Solution:
• Last digit = 3, Baaki = 12
• 3 × 2 = 6
• 12 - 6 = 6
• 6 ÷ 7 = not divisible → ✗ 123 not divisible by 7

💡 Alternative Method: Agar number bada ho, process repeat kar sakte ho.
Example: 1568 → 156 - (8×2) = 140 → 14 - 0 = 14 → Divisible by 7 ✓

7. Divisibility Rule for 8

🔹 Rule: Agar number ke last 3 digits 8 se divisible hain (ya 000 hain), toh wo number 8 se divisible hai.

Examples:

Example 1: Kya 12312 divisible by 8 hai?
Solution:
Last 3 digits = 312
312 ÷ 8 = 39 → ✓ Divisible by 8

Example 2: Kya 5438 divisible by 8 hai?
Solution:
Last 3 digits = 438
438 ÷ 8 = 54.75 → ✗ Not divisible by 8

✓ 1000 (000), 2128 (128÷8=16), 9016 (016÷8=2)
✗ 2345 (345÷8≠integer), 1111 (111÷8≠integer)

💡 Quick Check: Last 3 digits ko mentally 8 se divide karo. Agar exactly divisible ho, toh pura number bhi divisible hai.

8. Divisibility Rule for 9

🔹 Rule: Agar number ke sabhi digits ka sum 9 se divisible hai, toh wo number bhi 9 se divisible hai.

Examples:

Example 1: Kya 2583 divisible by 9 hai?
Solution:
Sum = 2 + 5 + 8 + 3 = 18
18 ÷ 9 = 2 → ✓ Divisible by 9

Example 2: Kya 1234 divisible by 9 hai?
Solution:
Sum = 1 + 2 + 3 + 4 = 10
10 ÷ 9 = 1.11 → ✗ Not divisible by 9

✓ 81 (8+1=9), 999 (9+9+9=27, 2+7=9), 1269 (1+2+6+9=18)
✗ 100 (1+0+0=1), 235 (2+3+5=10)

💡 Bonus Trick: Ye rule 3 ke divisibility ke similar hai, lekin sum 9 se divisible hona chahiye (not 3).

9. Divisibility Rule for 10

🔹 Rule: Agar number ka last digit 0 hai, toh wo number 10 se divisible hai.

Examples:

Example 1: 120, 1000, 99990 → ✓ Sab 10 se divisible

Example 2: 125, 238, 9995 → ✗ 10 se divisible nahi

💡 Sabse Simple Rule: Last digit = 0 → Divisible!

10. Divisibility Rule for 11 TRICKY

🔹 Rule: Odd positions ke digits ka sum - Even positions ke digits ka sum. Agar result 0 ya 11 ka multiple hai, toh number 11 se divisible hai.

Examples:

Example 1: Kya 1331 divisible by 11 hai?
Solution:
Odd positions (1st, 3rd): 1, 3 → Sum = 1 + 3 = 4
Even positions (2nd, 4th): 3, 1 → Sum = 3 + 1 = 4
Difference = 4 - 4 = 0 → ✓ Divisible by 11

Example 2: Kya 2728 divisible by 11 hai?
Solution:
Odd positions: 2, 2 → Sum = 4
Even positions: 7, 8 → Sum = 15
Difference = |4 - 15| = 11 → ✓ Divisible by 11

Example 3: Kya 1234 divisible by 11 hai?
Solution:
Odd positions: 1, 3 → Sum = 4
Even positions: 2, 4 → Sum = 6
Difference = |4 - 6| = 2 → ✗ Not divisible by 11

💡 Yaad Rakhne Ka Tarika:
Left se right: 1st digit - 2nd digit + 3rd digit - 4th digit...
Result 0 ya 11 ka multiple = Divisible!

Quick Reference Table – Sab Ek Saath

Number	Divisibility Rule	Example
2	Last digit even (0,2,4,6,8)	248 ✓ (last=8)
3	Sum of digits divisible by 3	123 ✓ (1+2+3=6)
4	Last 2 digits divisible by 4	1316 ✓ (16÷4=4)
5	Last digit 0 or 5	125 ✓ (last=5)
6	Divisible by both 2 and 3	132 ✓ (even & sum=6)
7	Last digit × 2, subtract from rest	203 ✓ (20-6=14)
8	Last 3 digits divisible by 8	2128 ✓ (128÷8=16)
9	Sum of digits divisible by 9	2583 ✓ (2+5+8+3=18)
10	Last digit is 0	120 ✓ (last=0)
11	Odd sum - Even sum = 0 or 11k	1331 ✓ (4-4=0)

SSC CGL Level Practice Questions

Q1. Niche diye numbers me se kaun 7 se divisible hai?
(A) 123 (B) 147 (C) 235 (D) 468

Answer: (B) 147
Solution: 14 - (7×2) = 14 - 14 = 0 → Divisible ✓

Q2. Agar ek number 2, 3, aur 5 teeno se divisible hai, toh wo kis sabse chhote number se bhi divisible hoga?
(A) 10 (B) 15 (C) 30 (D) 60

Answer: (C) 30
Solution: LCM(2,3,5) = 30

Q3. 3-digit number 47x agar 9 se divisible hai, toh x ki value kya hogi?
(A) 2 (B) 4 (C) 7 (D) 9

Answer: (C) 7
Solution: 4+7+x = 11+x → 9 se divisible hone ke liye → 11+x=18 → x=7

Q4. Kaun sa number dono 4 aur 6 se divisible hai?
(A) 24 (B) 18 (C) 20 (D) 30

Answer: (A) 24
Solution: 24 ÷ 4 = 6 ✓, 24 ÷ 6 = 4 ✓

Q5. 4-digit number 56x8 agar 11 se divisible hai, toh x ki value?
(A) 2 (B) 3 (C) 5 (D) 7

Answer: (D) 7
Solution:
Odd sum = 5+x = 5+x
Even sum = 6+8 = 14
Difference = |5+x-14| = |x-9|
x-9=0 or 11 → x=9 (not in options) ya 9-x=11 → Not possible
Try: 14-(5+x) = 0 or 11 → x=9 ya x= -2 (invalid)
Actually: (5+8)-(6+x) = 0 → 13-6-x=0 → x=7 ✓

Homework Practice (Khud Try Karo)

Kya 12648 divisible by 8 hai?
Kya 5643 divisible by 3 hai?
3-digit number 2x4 agar 6 se divisible hai, toh x ki possible values kya hongi?
Sabse chhota 4-digit number jo 11 se divisible ho?
Kya 987654 divisible by 9 hai?

Exam Tips & Memory Shortcuts

🎯 Exam Me Kaise Use Kare:

Speed badhane ke liye: 2, 5, 10 ke rules sabse fast hain
Accuracy ke liye: 3, 9 ke rules use karo (sum method reliable hai)
Tricky questions: 7, 11 ke rules practice karo (exam me zaroor aate hain)
Combined divisibility: 6 = 2 & 3, aise combinations yaad rakho

📝 Memory Mnemonics:
"2-5-10" → Last Digit Gang
"3-9" → Sum Wale Bhai
"4-8" → Last Multiple Digits (2 aur 3)
"7-11" → Formula Waale Heroes

Next Topic Preview

📚 Agle Post Me: 1.3 Prime Factorization
Prime factorization kaise karte hain, factor tree method, shortest method, aur iska HCF-LCM me use kaise hota hai – sab detail me padhenge!

Conclusion

Divisibility Rules number system ki neev hain. Ye rules SSC CGL me bahut kaam aate hain – directly questions me bhi aur indirectly HCF-LCM, simplification, aur speed calculation me bhi.

In rules ko practice karo daily. Har number dekhte hi mentally check karne ki aadat banao ki wo kisse divisible hai. Isse exam me speed aur accuracy dono badhegi!

✅ Post Complete! Classification of Numbers (1.1) ✅ | Divisibility Rules (1.2) ✅
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