Comprehensive math worksheet featuring 40 practice problems to test divisibility rules for numbers 2 through 10.

Let’s solve this step by step.

We are given 40 numbers, and for each one, we need to check which of these numbers it is divisible by:
2, 3, 5, 6, 9, 10

Here are the quick rules you can use:

- Divisible by 2? → Last digit is even (0, 2, 4, 6, 8)
- Divisible by 3? → Sum of digits is divisible by 3
- Divisible by 5? → Last digit is 0 or 5
- Divisible by 6? → Must be divisible by BOTH 2 and 3
- Divisible by 9? → Sum of digits is divisible by 9
- Divisible by 10? → Last digit is 0

Let’s go through each number one by one. I’ll write down the divisibility for each.

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1) 7580
Last digit = 0 → divisible by 2, 5, 10
Sum of digits: 7+5+8+0 = 20 → not divisible by 3 or 9 → so NOT divisible by 6
→ Divisible by: 2, 5, 10

2) 7583
Last digit = 3 → odd → not divisible by 2, 5, 10
Sum: 7+5+8+3 = 23 → not divisible by 3 or 9 → not divisible by 6
→ Divisible by: none

3) 7586
Last digit = 6 → even → divisible by 2
Sum: 7+5+8+6 = 26 → not divisible by 3 → not divisible by 6 or 9
Not ending in 0 or 5 → not divisible by 5 or 10
→ Divisible by: 2

4) 7590
Last digit = 0 → divisible by 2, 5, 10
Sum: 7+5+9+0 = 21 → divisible by 3 → so also divisible by 6
21 not divisible by 9 → not divisible by 9
→ Divisible by: 2, 3, 5, 6, 10

5) 7593
Last digit = 3 → odd → not divisible by 2, 5, 10
Sum: 7+5+9+3 = 24 → divisible by 3 → but not by 9 (24÷9=2.66…)
Since not divisible by 2 → not divisible by 6
→ Divisible by: 3

6) 7599
Last digit = 9 → odd → not divisible by 2, 5, 10
Sum: 7+5+9+9 = 30 → divisible by 3 → not by 9 (30÷9=3.33…)
Not divisible by 2 → not divisible by 6
→ Divisible by: 3

7) 7596
Last digit = 6 → even → divisible by 2
Sum: 7+5+9+6 = 27 → divisible by 3 and 9 → so divisible by 6 too
Not ending in 0 or 5 → not divisible by 5 or 10
→ Divisible by: 2, 3, 6, 9

8) 7603
Last digit = 3 → odd → not divisible by 2, 5, 10
Sum: 7+6+0+3 = 16 → not divisible by 3 or 9 → not divisible by 6
→ Divisible by: none

9) 7606
Last digit = 6 → even → divisible by 2
Sum: 7+6+0+6 = 19 → not divisible by 3 → not divisible by 6 or 9
Not ending in 0 or 5 → not divisible by 5 or 10
→ Divisible by: 2

10) 7609
Last digit = 9 → odd → not divisible by 2, 5, 10
Sum: 7+6+0+9 = 22 → not divisible by 3 or 9 → not divisible by 6
→ Divisible by: none

11) 7612
Last digit = 2 → even → divisible by 2
Sum: 7+6+1+2 = 16 → not divisible by 3 → not divisible by 6 or 9
Not ending in 0 or 5 → not divisible by 5 or 10
→ Divisible by: 2

12) 7616
Last digit = 6 → even → divisible by 2
Sum: 7+6+1+6 = 20 → not divisible by 3 → not divisible by 6 or 9
Not ending in 0 or 5 → not divisible by 5 or 10
→ Divisible by: 2

13) 7619
Last digit = 9 → odd → not divisible by 2, 5, 10
Sum: 7+6+1+9 = 23 → not divisible by 3 or 9 → not divisible by 6
→ Divisible by: none

14) 7622
Last digit = 2 → even → divisible by 2
Sum: 7+6+2+2 = 17 → not divisible by 3 → not divisible by 6 or 9
Not ending in 0 or 5 → not divisible by 5 or 10
→ Divisible by: 2

15) 7625
Last digit = 5 → divisible by 5
Odd → not divisible by 2, 10
Sum: 7+6+2+5 = 20 → not divisible by 3 → not divisible by 6 or 9
→ Divisible by: 5

16) 7629
Last digit = 9 → odd → not divisible by 2, 5, 10
Sum: 7+6+2+9 = 24 → divisible by 3 → not by 9 → not divisible by 6 (since not even)
→ Divisible by: 3

17) 7632
Last digit = 2 → even → divisible by 2
Sum: 7+6+3+2 = 18 → divisible by 3 and 9 → so divisible by 6
Not ending in 0 or 5 → not divisible by 5 or 10
→ Divisible by: 2, 3, 6, 9

18) 7635
Last digit = 5 → divisible by 5
Odd → not divisible by 2, 10
Sum: 7+6+3+5 = 21 → divisible by 3 → but not by 9 → not divisible by 6 (not even)
→ Divisible by: 3, 5

19) 7642
Last digit = 2 → even → divisible by 2
Sum: 7+6+4+2 = 19 → not divisible by 3 → not divisible by 6 or 9
Not ending in 0 or 5 → not divisible by 5 or 10
→ Divisible by: 2

20) 7639
Last digit = 9 → odd → not divisible by 2, 5, 10
Sum: 7+6+3+9 = 25 → not divisible by 3 or 9 → not divisible by 6
→ Divisible by: none

21) 7645
Last digit = 5 → divisible by 5
Odd → not divisible by 2, 10
Sum: 7+6+4+5 = 22 → not divisible by 3 → not divisible by 6 or 9
→ Divisible by: 5

22) 7648
Last digit = 8 → even → divisible by 2
Sum: 7+6+4+8 = 25 → not divisible by 3 → not divisible by 6 or 9
Not ending in 0 or 5 → not divisible by 5 or 10
→ Divisible by: 2

23) 7652
Last digit = 2 → even → divisible by 2
Sum: 7+6+5+2 = 20 → not divisible by 3 → not divisible by 6 or 9
Not ending in 0 or 5 → not divisible by 5 or 10
→ Divisible by: 2

24) 7655
Last digit = 5 → divisible by 5
Odd → not divisible by 2, 10
Sum: 7+6+5+5 = 23 → not divisible by 3 → not divisible by 6 or 9
→ Divisible by: 5

25) 7658
Last digit = 8 → even → divisible by 2
Sum: 7+6+5+8 = 26 → not divisible by 3 → not divisible by 6 or 9
Not ending in 0 or 5 → not divisible by 5 or 10
→ Divisible by: 2

26) 7661
Last digit = 1 → odd → not divisible by 2, 5, 10
Sum: 7+6+6+1 = 20 → not divisible by 3 or 9 → not divisible by 6
→ Divisible by: none

27) 7665
Last digit = 5 → divisible by 5
Odd → not divisible by 2, 10
Sum: 7+6+6+5 = 24 → divisible by 3 → not by 9 → not divisible by 6 (not even)
→ Divisible by: 3, 5

28) 7668
Last digit = 8 → even → divisible by 2
Sum: 7+6+6+8 = 27 → divisible by 3 and 9 → so divisible by 6
Not ending in 0 or 5 → not divisible by 5 or 10
→ Divisible by: 2, 3, 6, 9

29) 7671
Last digit = 1 → odd → not divisible by 2, 5, 10
Sum: 7+6+7+1 = 21 → divisible by 3 → not by 9 → not divisible by 6 (not even)
→ Divisible by: 3

30) 7674
Last digit = 4 → even → divisible by 2
Sum: 7+6+7+4 = 24 → divisible by 3 → not by 9 → so divisible by 6
Not ending in 0 or 5 → not divisible by 5 or 10
→ Divisible by: 2, 3, 6

31) 7678
Last digit = 8 → even → divisible by 2
Sum: 7+6+7+8 = 28 → not divisible by 3 → not divisible by 6 or 9
Not ending in 0 or 5 → not divisible by 5 or 10
→ Divisible by: 2

32) 7681
Last digit = 1 → odd → not divisible by 2, 5, 10
Sum: 7+6+8+1 = 22 → not divisible by 3 or 9 → not divisible by 6
→ Divisible by: none

33) 7684
Last digit = 4 → even → divisible by 2
Sum: 7+6+8+4 = 25 → not divisible by 3 → not divisible by 6 or 9
Not ending in 0 or 5 → not divisible by 5 or 10
→ Divisible by: 2

34) 7688
Last digit = 8 → even → divisible by 2
Sum: 7+6+8+8 = 29 → not divisible by 3 → not divisible by 6 or 9
Not ending in 0 or 5 → not divisible by 5 or 10
→ Divisible by: 2

35) 7691
Last digit = 1 → odd → not divisible by 2, 5, 10
Sum: 7+6+9+1 = 23 → not divisible by 3 or 9 → not divisible by 6
→ Divisible by: none

36) 7694
Last digit = 4 → even → divisible by 2
Sum: 7+6+9+4 = 26 → not divisible by 3 → not divisible by 6 or 9
Not ending in 0 or 5 → not divisible by 5 or 10
→ Divisible by: 2

37) 7697
Last digit = 7 → odd → not divisible by 2, 5, 10
Sum: 7+6+9+7 = 29 → not divisible by 3 or 9 → not divisible by 6
→ Divisible by: none

38) 7701
Last digit = 1 → odd → not divisible by 2, 5, 10
Sum: 7+7+0+1 = 15 → divisible by 3 → not by 9 → not divisible by 6 (not even)
→ Divisible by: 3

39) 7704
Last digit = 4 → even → divisible by 2
Sum: 7+7+0+4 = 18 → divisible by 3 and 9 → so divisible by 6
Not ending in 0 or 5 → not divisible by 5 or 10
→ Divisible by: 2, 3, 6, 9

40) 7707
Last digit = 7 → odd → not divisible by 2, 5, 10
Sum: 7+7+0+7 = 21 → divisible by 3 → not by 9 → not divisible by 6 (not even)
→ Divisible by: 3

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Final Answer:

1) 2, 5, 10
2) none
3) 2
4) 2, 3, 5, 6, 10
5) 3
6) 3
7) 2, 3, 6, 9
8) none
9) 2
10) none
11) 2
12) 2
13) none
14) 2
15) 5
16) 3
17) 2, 3, 6, 9
18) 3, 5
19) 2
20) none
21) 5
22) 2
23) 2
24) 5
25) 2
26) none
27) 3, 5
28) 2, 3, 6, 9
29) 3
30) 2, 3, 6
31) 2
32) none
33) 2
34) 2
35) none
36) 2
37) none
38) 3
39) 2, 3, 6, 9
40) 3