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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

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.

You can also use the Online Divisibility Calculator to check this.

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.3 Question 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) 2150 (i) 31795072 (j) 1700

Summary:

(a) Using divisibility test, we determined that 572 is divisible by 4 but not by 8. (b) Using divisibility test, we determined that 726352 is divisible by both 4 and 8. (c) Using divisibility test, we determined that 5500 is divisible by 4 but not by 8. (d) Using divisibility test, we determined that 6000 is divisible by both 4 and 8. (e) Using divisibility test, we determined that 12159 is neither divisible by 4 or 8. (f) Using divisibility test, we determined that 14560 is divisible by both 4 and 8. (g) Using divisibility test, we determined that 21084 is divisible by 4 but not by 8. (h) Using divisibility test, we determined that 31795072 is divisible by both 4 and 8. (i) Using divisibility test, we determined that 1700 is divisible by 4 but not by 8. (j)  Using the divisibility test, we determined that 2150 is neither divisible by 4 nor by 8.

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