Question

Делятся ли числа 600, 81, 3 330, 405, 9 034, 9 339, 75 870, 2 763, 480, 1 536, 12 521, 7 587 на: 1) 9; 2) 3?​

Answer 1

1) на 9 делятся числа, у которых сумма чисел делится на 9.

6+0+0=6

600 - не делится

8+1=9

81 - делится

3+3+3+0=9

3330 - делится

4+0+5=9

405 - делится

9+0+3+4=16

9034 - не делится

9+3+3+9=24

9339 - не делится

7+5+8+7+0=27

75870 - делится

4+8+0=12

480 - не делиться

1+5+3+6=15

1536 - не делится

1+2+5+2+1=11

12521 - не делится

7+5+8+7=27

7587 - делится

1) на 3 делятся числа, у которых сумма чисел делится на 3.

6+0+0=6

600 - делится

8+1=9

81 - делится

3+3+3+0=9

3330 - делится

4+0+5=9

405 - делится

9+0+3+4=16

9034 - не делится

9+3+3+9=24

9339 - делится

7+5+8+7+0=27

75870 - делится

4+8+0=12

480 - делиться

1+5+3+6=15

1536 - делится

1+2+5+2+1=11

12521 - не делится

7+5+8+7=27

7587 - делится

Answer 2

To determine if the given numbers are divisible by 9 and 3, we can check if the sum of their digits is divisible by 9 and 3, respectively. If the sum of the digits is divisible by 9, then the number itself is divisible by 9. Similarly, if the sum of the digits is divisible by 3, then the number itself is divisible by 3.

Let's calculate the sums of the digits for each number:

1. 600 → Sum of digits: 6 + 0 + 0 = 6
2. 81 → Sum of digits: 8 + 1 = 9
3. 3 330 → Sum of digits: 3 + 3 + 3 + 0 = 9
4. 405 → Sum of digits: 4 + 0 + 5 = 9
5. 9 034 → Sum of digits: 9 + 0 + 3 + 4 = 16
6. 9 339 → Sum of digits: 9 + 3 + 3 + 9 = 24
7. 75 870 → Sum of digits: 7 + 5 + 8 + 7 + 0 = 27
8. 2 763 → Sum of digits: 2 + 7 + 6 + 3 = 18
9. 480 → Sum of digits: 4 + 8 + 0 = 12
10. 1 536 → Sum of digits: 1 + 5 + 3 + 6 = 15
11. 12 521 → Sum of digits: 1 + 2 + 5 + 2 + 1 = 11
12. 7 587 → Sum of digits: 7 + 5 + 8 + 7 = 27

Now, let's check if each number is divisible by 9 and 3:

1. 600 → Divisible by 9: Yes, Divisible by 3: Yes
2. 81 → Divisible by 9: Yes, Divisible by 3: Yes
3. 3 330 → Divisible by 9: Yes, Divisible by 3: Yes
4. 405 → Divisible by 9: Yes, Divisible by 3: Yes
5. 9 034 → Divisible by 9: No, Divisible by 3: Yes
6. 9 339 → Divisible by 9: No, Divisible by 3: Yes
7. 75 870 → Divisible by 9: Yes, Divisible by 3: Yes
8. 2 763 → Divisible by 9: Yes, Divisible by 3: Yes
9. 480 → Divisible by 9: No, Divisible by 3: Yes
10. 1 536 → Divisible by 9: Yes, Divisible by 3: Yes
11. 12 521 → Divisible by 9: No, Divisible by 3: No
12. 7 587 → Divisible by 9: Yes, Divisible by 3: Yes

So, to summarize:

1. Divisible by 9: 600, 81, 3 330, 405, 75 870, 2 763, 1 536, 7 587
2. Divisible by 3: 600, 81, 3 330, 405, 9 339, 75 870, 2 763, 480, 1 536, 7 587

Note: If a number is divisible by 9, it is also divisible by 3. However, the reverse is not necessarily true. In this case, some numbers are divisible by 3 but not by 9 (e.g., 9 334) because they have a sum of digits that is divisible by 3 but not by 9.