Worksheet on divisibility test - Free Printable

Problem Analysis

The task involves determining the divisibility of given numbers by specific divisors (2, 3, 4, 5, 6, and 9) using the provided divisibility rules. Let's solve each question step by step.

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Divisibility Rules Recap:

1. Divisible by 2: The last digit is even.
2. Divisible by 3: The sum of the digits is divisible by 3.
3. Divisible by 4: The last two digits form a number divisible by 4.
4. Divisible by 5: The last digit is either 0 or 5.
5. Divisible by 6: The number is divisible by both 2 and 3.
6. Divisible by 9: The sum of the digits is divisible by 9.

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Solutions to Each Question

#### 1. 455 is divisible by _______
- Last digit: 5
- Rule for 5: A number is divisible by 5 if its last digit is 0 or 5.
- Conclusion: 455 is divisible by 5.

#### 2. 3939 is divisible by _______
- Sum of digits: \(3 + 9 + 3 + 9 = 24\)
- Rule for 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
- \(24 \div 3 = 8\) (exact division)
- Rule for 9: A number is divisible by 9 if the sum of its digits is divisible by 9.
- \(24 \div 9 = 2.67\) (not exact division)
- Conclusion: 3939 is divisible by 3.

#### 3. 2432 is divisible by _______
- Last digit: 2 (even)
- Rule for 2: A number is divisible by 2 if its last digit is even.
- Last two digits: 32
- Rule for 4: A number is divisible by 4 if the last two digits form a number divisible by 4.
- \(32 \div 4 = 8\) (exact division)
- Conclusion: 2432 is divisible by 2 and 4.

#### 4. 6273 is divisible by _______
- Sum of digits: \(6 + 2 + 7 + 3 = 18\)
- Rule for 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
- \(18 \div 3 = 6\) (exact division)
- Rule for 9: A number is divisible by 9 if the sum of its digits is divisible by 9.
- \(18 \div 9 = 2\) (exact division)
- Conclusion: 6273 is divisible by 3 and 9.

#### 5. If a number is divisible by 4, then it is also divisible by _______
- Rule for 4: A number divisible by 4 means its last two digits form a number divisible by 4.
- Implication: Any number divisible by 4 is also divisible by 2 (since 4 is a multiple of 2).
- Conclusion: If a number is divisible by 4, then it is also divisible by 2.

#### 6. 935050 is divisible by _______
- Last digit: 0
- Rule for 5: A number is divisible by 5 if its last digit is 0 or 5.
- Rule for 10: A number is divisible by 10 if its last digit is 0.
- Conclusion: 935050 is divisible by 5 and 10.

#### 7. 92454 is divisible by _______ and _______
- Last digit: 4 (even)
- Rule for 2: A number is divisible by 2 if its last digit is even.
- Sum of digits: \(9 + 2 + 4 + 5 + 4 = 24\)
- Rule for 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
- \(24 \div 3 = 8\) (exact division)
- Conclusion: 92454 is divisible by 2 and 3.

#### 8. 73384 is divisible by 2 and _______
- Last digit: 4 (even)
- Rule for 2: A number is divisible by 2 if its last digit is even.
- Last two digits: 84
- Rule for 4: A number is divisible by 4 if the last two digits form a number divisible by 4.
- \(84 \div 4 = 21\) (exact division)
- Conclusion: 73384 is divisible by 2 and 4.

#### 9. A number which is divisible by 10 is also divisible by _______
- Rule for 10: A number is divisible by 10 if its last digit is 0.
- Implication: Any number divisible by 10 is also divisible by 5 (since 10 is a multiple of 5).
- Conclusion: A number which is divisible by 10 is also divisible by 5.

#### 10. Give one number which is divisible by 6 _______
- Rule for 6: A number is divisible by 6 if it is divisible by both 2 and 3.
- Example: 12 (last digit is even → divisible by 2; sum of digits \(1 + 2 = 3\) → divisible by 3).
- Conclusion: One number divisible by 6 is 12.

#### 11. 9936 is divisible by _______
- Last digit: 6 (even)
- Rule for 2: A number is divisible by 2 if its last digit is even.
- Sum of digits: \(9 + 9 + 3 + 6 = 27\)
- Rule for 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
- \(27 \div 3 = 9\) (exact division)
- Rule for 6: A number is divisible by 6 if it is divisible by both 2 and 3.
- Conclusion: 9936 is divisible by 6.

#### 12. 899991 is divisible by _______ and _______
- Sum of digits: \(8 + 9 + 9 + 9 + 9 + 1 = 45\)
- Rule for 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
- \(45 \div 3 = 15\) (exact division)
- Rule for 9: A number is divisible by 9 if the sum of its digits is divisible by 9.
- \(45 \div 9 = 5\) (exact division)
- Conclusion: 899991 is divisible by 3 and 9.

#### 13. A number which is divisible by 2 and 3, is divisible by _______
- Rule for 6: A number is divisible by 6 if it is divisible by both 2 and 3.
- Conclusion: A number which is divisible by 2 and 3 is divisible by 6.

#### 14. If the last digit of a number is 0, then it is divisible by _______ and _______
- Rule for 10: A number is divisible by 10 if its last digit is 0.
- Rule for 5: A number is divisible by 5 if its last digit is 0 or 5.
- Conclusion: If the last digit of a number is 0, then it is divisible by 5 and 10.

#### 15. 1916 is divisible by 4. State true or false _______
- Last two digits: 16
- Rule for 4: A number is divisible by 4 if the last two digits form a number divisible by 4.
- \(16 \div 4 = 4\) (exact division)
- Conclusion: 1916 is divisible by 4. True.

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Final Answers

1. 5
2. 3
3. 2 and 4
4. 3 and 9
5. 2
6. 5 and 10
7. 2 and 3
8. 4
9. 5
10. 12
11. 6
12. 3 and 9
13. 6
14. 5 and 10
15. True

Boxed Answer:
\[
\boxed{5, 3, 2 \text{ and } 4, 3 \text{ and } 9, 2, 5 \text{ and } 10, 2 \text{ and } 3, 4, 5, 12, 6, 3 \text{ and } 9, 6, 5 \text{ and } 10, \text{True}}
\]