Question

using divisibility test determine which of the following numbers are divisible by 4 and 8
572 and 7 2 6 3 5 2 and 5500 and 6000 and 12159 and 14560 and 21084 and 31795072 and 1700 and 2150 ​
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Answer 1

According to the divisibility test of 4, a number is divisible by 4 only if it's last 2 digits are divisible by 4 or are 0.

1. 572- 72 is divisible by 4 (18). So the number is divisible by 4.

2. 726352- 52 is divisible by 4 (13). So the number is divisible by 4.

3. 5500- Since the last 2 digits are 0, the number is divisible by 4.

4. 6000- Since the last 2 digits are 0, the number is divisible by 4.

5. 12159- As the number is odd, without checking the last 2 digits we can say that the number is not divisible by 4.

6. 14560- 60 is divisible by 4 (15). So the number is divisible by 4.

7. 21084- 84 is divisible by 4 (21). So the number is divisible by 4.

8. 31795072- 72 is divisible by 4 (18). So the number is divisible by 4.

9. 1700- Since the last 2 digits are 0, the number is divisible by 4.

10. 2150- 50 is not divisible by 4. So the number is not divisible by 4.

Hope this helps you...

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Answer 2

Solution:

We will use the concept of divisibility by 4 and 8 to solve it

(a) Given number = 572

(i) Divisibility by 4

A number is divisible by 4 if the last two digits of the number are divisible by 4. Here, the last two digits of the given number are 7 and 2. Thus, we will check if 72 is divisible by 4:

72÷4 = 18

Quotient = 18 and remainder = 0. Therefore, 72 is divisible by 4 and so is 572 divisible by 4.

(ii) Divisibility by 8

A number is divisible by 8 if the last three digits of the number are divisible by 8. Here, the last three digits of the given number are 5, 7, and 2. Thus, we will check if 572 is divisible by 8:

Given number = 572

After performing division, we see that the remainder is 4. Therefore, 572 is not divisible by 8.

(b) Given number = 726352

(i) Divisibility by 4

Here, the last two digits of the given number are 5 and 2.

Thus, we will check if 52 is divisible by 4:

Given number = 726352

Remainder = 0.

Therefore, 52 is divisible by 4 and so is 726352.

(ii) Divisibility by 8

Here, the last three digits of the given number are 3, 5, and 2.

Thus, we will check if 352 is divisible by 8:

Given number = 726352

Remainder = 0.

Therefore, 352 is divisible by 8 and so is 726352.

(c) Given number = 5500

(i) Divisibility by 4

Here the last two digits of the given number are 00 which is divisible by 4. Hence, 5500 is divisible by 4.

(ii) Divisibility by 8

Here, the number formed by the last three digits of the given number = 500

Given number = 5500

Remainder = 4.

Therefore, 500 is not divisible by 8 and hence, 5500 is also not divisible by 8.

(d) Given number = 6000

(i) Divisibility by 4

Here, the last two digits of the given number are 00.

Therefore, 6000 is divisible by 4.

(ii) Divisibility by 8

Here, the last three digits of the given number are 000.

Therefore, 6000 is divisible by 8.

(e) Given number = 12159

(i) Divisibility by 4

Here, the last two digits of the given number are 5 and 9.

Thus, we will check if 59 is divisible by 4.

Given number = 12159

Remainder = 3.

Therefore, 59 is not divisible by 4 and hence 12159 is also not divisible by 4.

(ii) Divisibility by 8

Here, the last three digits of the given number are 1, 5, and 9. Thus, we will check if 159 is divisible by 8:

Given number = 12159

Remainder = 7.

Therefore, 159 is not divisible by 8 and hence12159 is also not divisible by 8.

(f) Given number = 14560

(i) Divisibility by 4

Here, the last two digits of the given number are 6 and 0.

Thus, we will check if 60 is divisible by 4:

Given number = 14560

Remainder = 0.

Therefore, 60 is divisible by 4 and so is 14560.

(ii) Divisibility by 8

Here, the last three digits of the given number are 5, 6, and 0. 560 ÷ 8 = 70.

Remainder = 0.

Therefore, 560 is divisible by 8 and so is 14560.

(g) Given number = 21084

(i) Divisibility by 4

Here, the last two digits of the given number are 8 and 4. Thus, we will check if 84 is divisible by 4:

Given number = 21084

Remainder = 0.

Therefore, 84 is divisible by 4 and so is 21084.

(ii) Divisibility by 8

Here, the last three digits of the given number are 0, 8, and 4.

Thus, we will check if 084 is divisible by 8:

Given number = 21084

Remainder = 4.

Therefore, 084 is not divisible by 8 and hence 21084 is not divisible by 8.

(h) Given number = 31795072

(i) Divisibility by 4

Here, the last two digits of the given number are 7 and 2.

Thus, we will check if 72 is divisible by 4:

Given number = 31795072

Remainder = 0.

Therefore, 72 is divisible by 4 and so is 31795072.

(ii) Divisibility by 8

Here, the last three digits of the given number are 0, 7, and 2.

Thus, we will check if 072 is divisible by 8.

Given number = 31795072

Remainder = 0.

Therefore, 072 is divisible by 8 and so is 31795072.

(i) Given number = 1700

Divisibility by 4

Here, the last two digits of the given number are 00. Hence, 1700 is divisible by 4.

(ii) Divisibility by 8

Here, the last three digits of the given number are 7, 0, and 0.

Thus, we will check if 700 is divisible by 8:

Given number = 1700

Remainder = 4.

Therefore, 700 is not divisible by 8 and hence 1700 is also not divisible by 8.

(j) Given number = 2150

(i) Divisibility by 4

Here, the last two digits of the given number are 5 and 0.

Thus, we will check if 50 is divisible by 4:

Given number = 2150

Remainder = 2.

Therefore, 50 is not divisible by 4 and hence 2150 is also not divisible by 4.

(ii) Divisibility by 8

Here, the last three digits of the given number are 1, 5, and 0.

Thus, we will check if 150 is divisible by 8:

Given number = 2150

Remainder = 6.

Therefore, 150 is not divisible by 8 and hence 2150 is also not divisible by 8.