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

To solve the problem, we need to apply the divisibility rules for each number listed in the table. Let's go through each number step by step and determine whether it is divisible by 2, 3, 4, 5, 6, 7, 8, or 9.

Divisibility Rules Recap:

1. By 2: The number must be even (last digit is 0, 2, 4, 6, or 8).
2. By 3: The sum of the digits must be divisible by 3.
3. By 4: The last two digits of the number must form a number divisible by 4.
4. By 5: The last digit must be 0 or 5.
5. By 6: The number must be divisible by both 2 and 3.
6. By 7: There is no simple rule; usually, direct division is required.
7. By 8: The last three digits of the number must form a number divisible by 8.
8. By 9: The sum of the digits must be divisible by 9.

Step-by-Step Analysis:

#### (i) 28
- By 2: Last digit is 8 (even) → Yes
- By 3: Sum of digits = 2 + 8 = 10 (not divisible by 3) → No
- By 4: Last two digits = 28 (divisible by 4) → Yes
- By 5: Last digit is not 0 or 5 → No
- By 6: Not divisible by 3 → No
- By 7: 28 ÷ 7 = 4 (exact) → Yes
- By 8: Last three digits = 028 (not divisible by 8) → No
- By 9: Sum of digits = 10 (not divisible by 9) → No

#### (ii) 36
- By 2: Last digit is 6 (even) → Yes
- By 3: Sum of digits = 3 + 6 = 9 (divisible by 3) → Yes
- By 4: Last two digits = 36 (divisible by 4) → 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 (not exact) → No
- By 8: Last three digits = 036 (not divisible by 8) → No
- By 9: Sum of digits = 9 (divisible by 9) → Yes

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

#### (iv) 144
- By 2: Last digit is 4 (even) → Yes
- By 3: Sum of digits = 1 + 4 + 4 = 9 (divisible by 3) → Yes
- By 4: Last two digits = 44 (divisible by 4) → 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 (not exact) → No
- By 8: Last three digits = 144 (divisible by 8) → Yes
- By 9: Sum of digits = 9 (divisible by 9) → Yes

#### (v) 303
- By 2: Last digit is 3 (odd) → No
- By 3: Sum of digits = 3 + 0 + 3 = 6 (divisible by 3) → Yes
- By 4: Last two digits = 03 (not divisible by 4) → No
- By 5: Last digit is not 0 or 5 → No
- By 6: Not divisible by 2 → No
- By 7: 303 ÷ 7 = 43.29 (not exact) → No
- By 8: Last three digits = 303 (not divisible by 8) → No
- By 9: Sum of digits = 6 (not divisible by 9) → No

#### (vi) 756
- By 2: Last digit is 6 (even) → Yes
- By 3: Sum of digits = 7 + 5 + 6 = 18 (divisible by 3) → Yes
- By 4: Last two digits = 56 (divisible by 4) → 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 (exact) → Yes
- By 8: Last three digits = 756 (divisible by 8) → Yes
- By 9: Sum of digits = 18 (divisible by 9) → Yes

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

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

#### (ix) 1455
- By 2: Last digit is 5 (odd) → No
- By 3: Sum of digits = 1 + 4 + 5 + 5 = 15 (divisible by 3) → Yes
- By 4: Last two digits = 55 (not divisible by 4) → No
- By 5: Last digit is 5 → Yes
- By 6: Not divisible by 2 → No
- By 7: 1455 ÷ 7 = 207.86 (not exact) → No
- By 8: Last three digits = 455 (not divisible by 8) → No
- By 9: Sum of digits = 15 (not divisible by 9) → No

Final Answer:

\[
\boxed{
\begin{array}{|c|c|c|c|c|c|c|c|c|}
\hline
& \text{Number} & \text{By 2} & \text{By 3} & \text{By 4} & \text{By 5} & \text{By 6} & \text{By 7} & \text{By 8} & \text{By 9} \\
\hline
(i) & 28 & \text{Yes} & \text{No} & \text{Yes} & \text{No} & \text{No} & \text{Yes} & \text{No} & \text{No} \\
(ii) & 36 & \text{Yes} & \text{Yes} & \text{Yes} & \text{No} & \text{Yes} & \text{No} & \text{No} & \text{Yes} \\
(iii) & 56 & \text{Yes} & \text{No} & \text{Yes} & \text{No} & \text{No} & \text{Yes} & \text{Yes} & \text{No} \\
(iv) & 144 & \text{Yes} & \text{Yes} & \text{Yes} & \text{No} & \text{Yes} & \text{No} & \text{Yes} & \text{Yes} \\
(v) & 303 & \text{No} & \text{Yes} & \text{No} & \text{No} & \text{No} & \text{No} & \text{No} & \text{No} \\
(vi) & 756 & \text{Yes} & \text{Yes} & \text{Yes} & \text{No} & \text{Yes} & \text{Yes} & \text{Yes} & \text{Yes} \\
(vii) & 1000 & \text{Yes} & \text{No} & \text{Yes} & \text{Yes} & \text{No} & \text{No} & \text{Yes} & \text{No} \\
(viii) & 8000 & \text{Yes} & \text{No} & \text{Yes} & \text{Yes} & \text{No} & \text{No} & \text{Yes} & \text{No} \\
(ix) & 1455 & \text{No} & \text{Yes} & \text{No} & \text{Yes} & \text{No} & \text{No} & \text{No} & \text{No} \\
\hline
\end{array}
}
\]