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 do :

We have to find whether the given numbers are divisible by 4 and by 8.

Solution :

Divisibility by 4

If the last two digits of a number are divisible by 4, then that number is a multiple of 4 and is divisible by 4 completely.

(a) In 572, 72 is divisible by 4.

Therefore, 572 is divisible by 4.

572 is not divisible by 8.

(b) In 726352, 72 is divisible by 4.

Therefore, 726352 is divisible by 4.

In 726352, 352 is divisible by 8.

Therefore, 726352 is divisible by 8.

(c) In 5500, 00 is divisible by 4.

Therefore, 5500 is divisible by 4.

In 5500, 500 is not divisible by 8.

Therefore, 5500 is not divisible by 8.

(d) In 6000, 00 is divisible by 4.

Therefore, 6000 is divisible by 4.

In 6000, 000 is divisible by 8.

Therefore, 6000 is divisible by 8.

(e) In 12159, 59 is not divisible by 4.

Therefore, 12159 is not divisible by 4.

In 12159, 159 is not divisible by 8.

Therefore, 12159 is not divisible by 8.

(f) In 14560, 60 is divisible by 4.

Therefore, 14560 is divisible by 4.

In 14560, 560 is divisible by 8.

Therefore, 14560 is divisible by 8.

(g) In 21084, 84 is divisible by 4.

Therefore, 21084 is divisible by 4.

In 21084, 084 is not divisible by 8.

Therefore, 21084 is not divisible by 8.

(h) In 31795072, 72 is divisible by 4.

Therefore, 31795072 is divisible by 4.

In 31795072, 072 is divisible by 8.

Therefore, 31795072 is divisible by 8.

(i) In 1700, 00 is divisible by 4.

Therefore, 1700 is divisible by 4.

In 1700, 700 is not divisible by 8.

Therefore, 1700 is not divisible by 8.

(j) In 2150, 50 is not divisible by 4.

Therefore, 2150 is not divisible by 4.

In 2150, 150 is not divisible by 8.

Therefore, 2150 is not divisible by 8.