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Divisibility Rules

Here are the rules to check if a number is divisible by another number:

Divisible by Rule Example
2 The last digit is 0, 2, 4, 6, or 8. 130 (ends with 0), 128 (ends with 8).
3 Add all digits. If the sum is divisible by 3, the number is too. 6561: 6+5+6+1 = 18 (divisible by 3).
4 The last two digits are 00 or divisible by 4. 17400 (ends with 00), 132 (32 ÷ 4 = 8).
5 The last digit is 0 or 5. 895 (ends with 5), 100 (ends with 0).
6 The number is divisible by both 2 and 3. 24 (divisible by 2 and 3).
7 Multiply the last digit by 5 and add it to the rest. If divisible by 7, the number is too. 105: 10 + (5×5) = 35 (divisible by 7).
8 The last three digits are 000 or divisible by 8. 125128 (128 ÷ 8 = 16).
9 Add all digits. If the sum is divisible by 9, the number is too. 729: 7+2+9 = 18 (divisible by 9).
10 The last digit is 0. 100, 23450 (both end with 0).
11 Subtract the sum of digits in odd places from the sum of digits in even places. If the result is 0 or divisible by 11, the number is too. 65967: (6+9+7) - (5+6) = 11 (divisible by 11).
13 Multiply the last digit by 4 and add it to the rest. Repeat if needed. If the result is divisible by 13, the number is too. 3146: 314 + (6×4) = 338 → 33 + (8×4) = 65 (divisible by 13).
17 Multiply the last digit by 5 and subtract it from the rest. Repeat if needed. If the result is divisible by 17, the number is too. 2278: 227 - (8×5) = 187 (divisible by 17).
19 Multiply the last digit by 2 and add it to the rest. Repeat if needed. If the result is divisible by 19, the number is too. 11343: 1134 + (3×2) = 1140 → 11 + (4×2) = 19 (divisible by 19).

Practice MCQs:

1. Which of the following numbers is divisible by 2?

  1. 123
  2. 456
  3. 789
  4. 101

Answer: B) 456

2. Which of the following numbers is divisible by 3?

  1. 112
  2. 234
  3. 457
  4. 678

Answer: B) 234

3. Which of the following numbers is divisible by 5?

  1. 123
  2. 450
  3. 678
  4. 789

Answer: B) 450

4. Which of the following numbers is divisible by 6?

  1. 123
  2. 456
  3. 789
  4. 101

Answer: B) 456

5. Which of the following numbers is divisible by 9?

  1. 123
  2. 456
  3. 729
  4. 101

Answer: C) 729

6. Which of the following numbers is divisible by 11?

  1. 121
  2. 234
  3. 456
  4. 789

Answer: A) 121

7. Which of the following numbers is divisible by 13?

  1. 169
  2. 234
  3. 456
  4. 789

Answer: A) 169

8. Which of the following numbers is divisible by 17?

  1. 153
  2. 234
  3. 289
  4. 456

Answer: C) 289

9. Which of the following numbers is divisible by 19?

  1. 171
  2. 234
  3. 456
  4. 789

Answer: A) 171

10. Which of the following numbers is divisible by 4?

  1. 123
  2. 456
  3. 789
  4. 101

Answer: B) 456