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# Using divisibility test, determine which of the following numbers are divisibly by 4, by 8 (a) 572 (b) 726352 (c) 5500 (d) 6000 (e) 12159 (f) 14560 (g) 21084 (h) 31795072 (i) 1700 (j) 2150

A divisibility rule is a kind of shortcut to figure out if a given integer is divisible by a divisor, without performing the whole division process but by examining its digits.

## Answer: The numbers which are divisible by 4 are a), b), c), d), f), g), h) and i) while the numbers divisible by 8 are b),d),f) and h).

The divisibility rule of 4 is: check the last 2 digits of a number and if its divisible by 4 then the given number is also divisible by 4.

The divisibility rule of 8 is: check the last 3 digits of a number and if its divisible by 8 then the given number is divisible by 8.

**Explanation:**

572, last 2 digits - 72, last 3 digits - 572, divisible by 4 but not by 8 as 72 is a multiple of 4 but 572 is not a multiple of 8.

726352, last 2 digits - 52, last 3 digits - 352, divisible by 4 and by 8 as 52 is a multiple of 4 and 352 is a multiple of 8.

5500, last 2 digits - 00, last 3 digits - 500, divisible by 4 but not by 8 as 0 is a multiple of 4 but 500 is not a multiple of 8.

6000, last 2 digits - 00, last 3 digits - 000, divisible by 4 and by 8 as 0 is a multiple of both 4 and 8.

12159, last 2 digits - 59, last 3 digits - 159, not divisible by 4 and 8 as 59 and 159 are not the multiples of 4 and 8 respectively.

14560, last 2 digits - 60, last 3 digits - 560, divisible by 4 and by 8 as 60 is a multiple of 4 and 560 is a multiple of 8.

21084, last 2 digits - 84, last 3 digits - 084, divisible by 4 but not by 8 as 84 is a multiple of 4 but not a multiple of 8.

31795072, last 2 digits - 72, last 3 digits - 072, divisible by 4 and by 8 as 72 is a multiple of both 4 and 8.

1700, last 2 digits - 00, last 3 digits - 700, divisible by 4 but not by 8 as 0 is a multiple of 4 but 700 is not a multiple of 8.

2150, last 2 digits - 50, last 3 digits - 150, not divisible by 4 and 8 as 50 and 150 are not the multiples of 4 and 8 respectively.

### Thus, the numbers which are divisible by 4 are: a), b), c), d), f), g), h) and i) while the numbers divisible by 8 are: b),d),f) and h).

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