Worksheet on Divisibility Rules | Questions on Test of Divisibility - Free Printable

This image presents a table for applying divisibility rules. The task is to fill in the empty cells with "Yes" or "No" based on whether each number in the first column is divisible by the numbers 2, 3, 4, 5, 6, 7, 8, and 9.

I will solve this problem by applying the standard divisibility rules for each number.

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Divisibility Rules Recap:

- By 2: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, 8).
- By 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
- By 4: A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
- By 5: A number is divisible by 5 if its last digit is 0 or 5.
- By 6: A number is divisible by 6 if it is divisible by both 2 and 3.
- By 7: There is no simple rule; we can divide the number by 7 to check.
- By 8: A number is divisible by 8 if the number formed by its last three digits is divisible by 8.
- By 9: A number is divisible by 9 if the sum of its digits is divisible by 9.

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Step-by-step Solution:

#### (i) Number: 28
- By 2: Last digit is 8 → Yes
- By 3: 2 + 8 = 10, not divisible by 3 → No
- By 4: Last two digits are 28, 28 ÷ 4 = 7 → Yes (already given)
- By 5: Last digit is not 0 or 5 → No
- By 6: Not divisible by both 2 and 3 → No
- By 7: 28 ÷ 7 = 4 → Yes
- By 8: Last three digits are 028, 28 ÷ 8 = 3.5 → No
- By 9: Sum of digits is 10, not divisible by 9 → No

#### (ii) Number: 36
- By 2: Last digit is 6 → Yes
- By 3: 3 + 6 = 9, divisible by 3 → Yes
- By 4: Last two digits are 36, 36 ÷ 4 = 9 → Yes
- By 5: Last digit is not 0 or 5 → No
- By 6: Divisible by both 2 and 3 → Yes
- By 7: 36 ÷ 7 ≈ 5.14 → No
- By 8: Last three digits are 036, 36 ÷ 8 = 4.5 → No
- By 9: Sum of digits is 9, divisible by 9 → Yes

#### (iii) Number: 56
- By 2: Last digit is 6 → Yes
- By 3: 5 + 6 = 11, not divisible by 3 → No
- By 4: Last two digits are 56, 56 ÷ 4 = 14 → Yes
- By 5: Last digit is not 0 or 5 → No
- By 6: Not divisible by both 2 and 3 → No
- By 7: 56 ÷ 7 = 8 → Yes
- By 8: Last three digits are 056, 56 ÷ 8 = 7 → Yes
- By 9: Sum of digits is 11, not divisible by 9 → No

#### (iv) Number: 144
- By 2: Last digit is 4 → Yes
- By 3: 1 + 4 + 4 = 9, divisible by 3 → Yes
- By 4: Last two digits are 44, 44 ÷ 4 = 11 → Yes
- By 5: Last digit is not 0 or 5 → No
- By 6: Divisible by both 2 and 3 → Yes
- By 7: 144 ÷ 7 ≈ 20.57 → No
- By 8: Last three digits are 144, 144 ÷ 8 = 18 → Yes
- By 9: Sum of digits is 9, divisible by 9 → Yes

#### (v) Number: 303
- By 2: Last digit is 3 → No
- By 3: 3 + 0 + 3 = 6, divisible by 3 → Yes
- By 4: Last two digits are 03, 3 ÷ 4 = 0.75 → No
- By 5: Last digit is not 0 or 5 → No
- By 6: Not divisible by both 2 and 3 → No
- By 7: 303 ÷ 7 ≈ 43.29 → No (already given as "NO")
- By 8: Last three digits are 303, 303 ÷ 8 = 37.875 → No
- By 9: Sum of digits is 6, not divisible by 9 → No

#### (vi) Number: 756
- By 2: Last digit is 6 → Yes
- By 3: 7 + 5 + 6 = 18, divisible by 3 → Yes
- By 4: Last two digits are 56, 56 ÷ 4 = 14 → Yes
- By 5: Last digit is not 0 or 5 → No
- By 6: Divisible by both 2 and 3 → Yes
- By 7: 756 ÷ 7 = 108 → Yes
- By 8: Last three digits are 756, 756 ÷ 8 = 94.5 → No
- By 9: Sum of digits is 18, divisible by 9 → Yes

#### (vii) Number: 1000
- By 2: Last digit is 0 → Yes
- By 3: 1 + 0 + 0 + 0 = 1, not divisible by 3 → No
- By 4: Last two digits are 00, 0 ÷ 4 = 0 → Yes
- By 5: Last digit is 0 → Yes
- By 6: Not divisible by both 2 and 3 → No
- By 7: 1000 ÷ 7 ≈ 142.86 → No
- By 8: Last three digits are 000, 0 ÷ 8 = 0 → Yes
- By 9: Sum of digits is 1, not divisible by 9 → No

#### (viii) Number: 8000
- By 2: Last digit is 0 → Yes
- By 3: 8 + 0 + 0 + 0 = 8, not divisible by 3 → No
- By 4: Last two digits are 00, 0 ÷ 4 = 0 → Yes
- By 5: Last digit is 0 → Yes
- By 6: Not divisible by both 2 and 3 → No
- By 7: 8000 ÷ 7 ≈ 1142.86 → No
- By 8: Last three digits are 000, 0 ÷ 8 = 0 → Yes
- By 9: Sum of digits is 8, not divisible by 9 → No

#### (ix) Number: 1455
- By 2: Last digit is 5 → No
- By 3: 1 + 4 + 5 + 5 = 15, divisible by 3 → Yes
- By 4: Last two digits are 55, 55 ÷ 4 = 13.75 → No
- By 5: Last digit is 5 → Yes (already given)
- By 6: Not divisible by both 2 and 3 → No
- By 7: 1455 ÷ 7 ≈ 207.86 → No
- By 8: Last three digits are 455, 455 ÷ 8 = 56.875 → No
- By 9: Sum of digits is 15, not divisible by 9 → No

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Final Answer:

Here is the completed table:

| | Number | By 2 | By 3 | By 4 | By 5 | By 6 | By 7 | By 8 | By 9 |
|-------|--------|------|------|------|------|------|------|------|------|
| (i) | 28 | Yes | No | Yes | No | No | Yes | No | No |
| (ii) | 36 | Yes | Yes | Yes | No | Yes | No | No | Yes |
| (iii) | 56 | Yes | No | Yes | No | No | Yes | Yes | No |
| (iv) | 144 | Yes | Yes | Yes | No | Yes | No | Yes | Yes |
| (v) | 303 | No | Yes | No | No | No | No | No | No |
| (vi) | 756 | Yes | Yes | Yes | No | Yes | Yes | No | Yes |
| (vii) | 1000 | Yes | No | Yes | Yes | No | No | Yes | No |
| (viii)| 8000 | Yes | No | Yes | Yes | No | No | Yes | No |
| (ix) | 1455 | No | Yes | No | Yes | No | No | No | No |

This completes the task.