Let's solve this step by step using
divisibility rules for the numbers 2, 3, 4, 5, 6, 9, and 10.
---
🔹 Divisibility Rules:
-
2: Number ends in an even digit (0, 2, 4, 6, 8).
-
3: Sum of digits is divisible by 3.
-
4: Last two digits form a number divisible by 4.
-
5: Ends in 0 or 5.
-
6: Divisible by both 2 and 3.
-
9: Sum of digits is divisible by 9.
-
10: Ends in 0.
---
We'll go through each number:
---
1. 76,455
- Ends in
5 → divisible by
5
- Sum of digits: 7+6+4+5+5 =
27 → divisible by
3 and
9
- Not even → not divisible by
2,
4,
6,
10
-
✔ Divisible by:
3, 5, 9
---
2. 927
- Ends in
7 → odd → not divisible by
2, 4, 6, 10
- Sum: 9+2+7 =
18 → divisible by
3 and
9
- Does not end in 0 or 5 → not divisible by
5
-
✔ Divisible by:
3, 9
---
3. 8,136
- Ends in
6 → even → divisible by
2
- Last two digits:
36 → divisible by
4 →
✔
- Sum: 8+1+3+6 =
18 → divisible by
3 and
9
- Since divisible by
2 and
3 → divisible by
6
- Doesn't end in 0 or 5 → not divisible by
5 or
10
-
✔ Divisible by:
2, 3, 4, 6, 9
---
4. 35,421
- Ends in
1 → odd → not divisible by
2, 4, 6, 10
- Sum: 3+5+4+2+1 =
15 → divisible by
3, but not by
9
- Doesn’t end in 0 or 5 → not divisible by
5
-
✔ Divisible by:
3
---
5. 91,350
- Ends in
0 → divisible by
2, 5, 10
- Last two digits:
50 → divisible by
2 and 5, but 50 ÷ 4 = 12.5 → not divisible by
4
- Sum: 9+1+3+5+0 =
18 → divisible by
3 and
9
- Since divisible by
2 and
3 → divisible by
6
-
✔ Divisible by:
2, 3, 5, 6, 9, 10
---
6. 240
- Ends in
0 → divisible by
2, 5, 10
- Last two digits:
40 → divisible by
4
- Sum: 2+4+0 =
6 → divisible by
3
- Divisible by
2 and
3 → divisible by
6
-
✔ Divisible by:
2, 3, 4, 5, 6, 10
---
7. 1,435
- Ends in
5 → divisible by
5
- Odd → not divisible by
2, 4, 6, 10
- Sum: 1+4+3+5 =
13 → not divisible by
3 or
9
-
✔ Divisible by:
5
---
8. 65,736
- Ends in
6 → even → divisible by
2
- Last two digits:
36 → divisible by
4
- Sum: 6+5+7+3+6 =
27 → divisible by
3 and
9
- Divisible by
2 and
3 → divisible by
6
- Doesn't end in 0 or 5 → not divisible by
5 or
10
-
✔ Divisible by:
2, 3, 4, 6, 9
---
✔ Final Answer Table:
| Number | 2 | 3 | 4 | 5 | 6 | 9 | 10 |
|-----------|---|---|---|---|---|---|----|
| 76,455 | |
✔ | |
✔ | |
✔ | |
| 927 | |
✔ | | | |
✔ | |
| 8,136 |
✔ |
✔ |
✔ | |
✔ |
✔ | |
| 35,421 | |
✔ | | | | | |
| 91,350 |
✔ |
✔ | |
✔ |
✔ |
✔ |
✔ |
| 240 |
✔ |
✔ |
✔ |
✔ |
✔ | |
✔ |
| 1,435 | | | |
✔ | | | |
| 65,736 |
✔ |
✔ |
✔ | |
✔ |
✔ | |
---
✔ Explanation Summary:
Each check mark was placed based on applying the divisibility rules above. For example:
- A number ending in 0 or 5 is divisible by 5.
- If the sum of digits is divisible by 3, it’s divisible by 3.
- Even numbers are divisible by 2.
- And so on.
This method avoids long division and helps quickly determine factors!
Parent Tip: Review the logic above to help your child master the concept of divisibility rules worksheet.
