Answered

2. Using divisibility tests, determine which of the following numbers are divisible by 4; by 8:

(a) 572
(b) 726352
(c) 5500
(d) 6000
(e) 12159
(f) 14560
(g) 21084
(h) 31795072



Answer :

GinnyAnswer
Certainly! Let's determine the numbers that are divisible by 4 and by 8.

### Divisibility by 4:
A number is divisible by 4 if the last two digits of the number are divisible by 4.

1. 572
- Last two digits: 72
- 72 is divisible by 4.
- Result: Divisible by 4

2. 14560
- Last two digits: 60
- 60 is divisible by 4.
- Result: Divisible by 4

3. 726352
- Last two digits: 52
- 52 is divisible by 4.
- Result: Divisible by 4

4. 5500
- Last two digits: 00
- 00 is divisible by 4.
- Result: Divisible by 4

5. 21084
- Last two digits: 84
- 84 is divisible by 4.
- Result: Divisible by 4

6. 31795072
- Last two digits: 72
- 72 is divisible by 4.
- Result: Divisible by 4

7. 6000
- Last two digits: 00
- 00 is divisible by 4.
- Result: Divisible by 4

8. 1700
- Last two digits: 00
- 00 is divisible by 4.
- Result: Divisible by 4

9. 12159
- Last two digits: 59
- 59 is not divisible by 4.
- Result: Not divisible by 4

10. 2150
- Last two digits: 50
- 50 is not divisible by 4.
- Result: Not divisible by 4

So, the numbers from the list that are divisible by 4 are:
- 572, 14560, 726352, 5500, 21084, 31795072, 6000, and 1700.

### Divisibility by 8:
A number is divisible by 8 if the last three digits of the number are divisible by 8.

1. 572
- Last three digits: 572
- 572 is not divisible by 8.
- Result: Not divisible by 8

2. 14560
- Last three digits: 560
- 560 is divisible by 8.
- Result: Divisible by 8

3. 726352
- Last three digits: 352
- 352 is divisible by 8.
- Result: Divisible by 8

4. 5500
- Last three digits: 500
- 500 is not divisible by 8.
- Result: Not divisible by 8

5. 21084
- Last three digits: 084
- 084 is not divisible by 8.
- Result: Not divisible by 8

6. 31795072
- Last three digits: 072
- 072 is divisible by 8.
- Result: Divisible by 8

7. 6000
- Last three digits: 000
- 000 is divisible by 8.
- Result: Divisible by 8

8. 1700
- Last three digits: 700
- 700 is not divisible by 8.
- Result: Not divisible by 8

9. 12159
- Last three digits: 159
- 159 is not divisible by 8.
- Result: Not divisible by 8

10. 2150
- Last three digits: 150
- 150 is not divisible by 8.
- Result: Not divisible by 8

So, the numbers from the list that are divisible by 8 are:
- 14560, 726352, 31795072, and 6000.

### Summary:
- Divisible by 4: 572, 14560, 726352, 5500, 21084, 31795072, 6000, and 1700.
- Divisible by 8: 14560, 726352, 31795072, and 6000.