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            (i) 1700              (j) 2150

To check whether the above number are divisible by 4 or 8, we will use the following divisibility rule.

Divisibility by 4: If the sum of the last two digits, or ones and tens, of a number with 3 or more digits is also divisible by 4, then the number is divisible by 4.

Divisibility by 8: If the sum of the final three digits is a number that can be divided by 8, then the number is divisible by 8.

(a) 572
The final two digits are 72, as 72 can be divided by 4. Therefore, 572 can be divided by 4.
Since 572 is the last three digits, it is also divisible by 4. As 572 cannot be divided by 8. Therefore, 572 cannot be divided by 8.

(b) 726352
The final two digits are 52. 52 can be divided by 4. Therefore, 726352 can be divided by 4.
The final three digits are 352. 352 can be divided by 8. Therefore, 726352 can be divided by 8.

(c) 5500
Since 00 is the last two digits. Therefore, 5500 is divisible by 4.
The final three digits are 500. As 500 cannot be divided by 8. Therefore, 5500 cannot be divided by 8.

(d) 6000
Since 00 is the last two digits. Therefore, 6000 is divisible by 4.
Since 000 is the final three digits. Therefore, 6000 can be divided by 8.

(e) 12159
The final two digits are 59. As 59 cannot be divided by 4. Therefore, 12159 cannot be divided by 4.
The final three digits are 159. As 159 cannot be divided by 8. Therefore, 12159 cannot be divided by 8.

(f) 14560
The final two digits are 60. Therefore, 14560 is divisible by 4.
The final three digits are 560. Therefore, 14560 is divisible by 8.

(g) 21084
The final two digits are 84. 84 can be divided by 4. Therefore, 21084 is divisible by 4.
The final three digits are 084. As 084 cannot be divided by 8. Therefore, 21084 cannot be divided by 8.

(h) 31795072
The final two digits are 72. As 72 can be divided by 4.  Therefore, 31795072 is divisible by 4.
The final three digits are 072. As 072 is divisible by 8. Therefore, 31795072 is divisible by 8.

(i) 1700
Since 1700 has the last two digits of 00, it can be divided by 4.
The final three digits are 700. As 700 cannot be divided by 8. Therefore, 1700 cannot be divided by 8.

(j) 2150
The final two digits are 50. As 50 cannot be divided by 4. Therefore, 2150 cannot be divided by 4.
The final three digits are 150. As 150 cannot be divided by 8. Therefore, 2150 cannot be divided by 8.