RS Aggarwal Solutions: Exercise 5B - Playing With Numbers | Mathematics (Maths) Class 8 PDF Download

 Page 1


   
  
    
      
  
      
  
    
Question:7
Test the divisibility of each of the following numers by 2:
i
94
ii
570
iii
285
iv
2398
v
79532
vi
13576
vii
46821
viii
84663
ix
66669
Solution:
A given number is divisible by 2 only when its unit digit is 0, 2, 4, 6 or 8.
i
94
The number 94 has '4' at its unit's place so, it is divisible by 2.
ii
570
The number 570 has '0' at its unit's place so, it is divisible by 2.
iii
285
The number 285 has '5' at its unit's place so, it is not divisible by 2.
iv
2398
The number 2398 has '8' at its unit's place so, it is divisible by 2.
v
79532
The number 79532 has '2' at its unit's place so, it is divisible by 2.
vi
13576
The number 13576 has '6' at its unit's place so, it is divisible by 2.
vii
46821
The number 46821 has '1' at its unit's place so, it is not divisible by 2.
viii
84663
The number 84663 has '3' at its unit's place so, it is not divisible by 2.
ix
66669
The number 66669 has '9' at its unit's place so, it is not divisible by 2.
Question:8
Test the divisibility of each of the following numers by 5:
i
95
ii
470
iii
1056
iv
2735
v
55053
vi
35790
vii
98765
viii
42658
ix
77990
Solution:
A given number is divisible by 5 only when its unit digit is 0 or 5.
i
95
Page 2


   
  
    
      
  
      
  
    
Question:7
Test the divisibility of each of the following numers by 2:
i
94
ii
570
iii
285
iv
2398
v
79532
vi
13576
vii
46821
viii
84663
ix
66669
Solution:
A given number is divisible by 2 only when its unit digit is 0, 2, 4, 6 or 8.
i
94
The number 94 has '4' at its unit's place so, it is divisible by 2.
ii
570
The number 570 has '0' at its unit's place so, it is divisible by 2.
iii
285
The number 285 has '5' at its unit's place so, it is not divisible by 2.
iv
2398
The number 2398 has '8' at its unit's place so, it is divisible by 2.
v
79532
The number 79532 has '2' at its unit's place so, it is divisible by 2.
vi
13576
The number 13576 has '6' at its unit's place so, it is divisible by 2.
vii
46821
The number 46821 has '1' at its unit's place so, it is not divisible by 2.
viii
84663
The number 84663 has '3' at its unit's place so, it is not divisible by 2.
ix
66669
The number 66669 has '9' at its unit's place so, it is not divisible by 2.
Question:8
Test the divisibility of each of the following numers by 5:
i
95
ii
470
iii
1056
iv
2735
v
55053
vi
35790
vii
98765
viii
42658
ix
77990
Solution:
A given number is divisible by 5 only when its unit digit is 0 or 5.
i
95
The number 95 has '5' at its unit's place so, it is divisible by 5.
ii
470
The number 470 has '0' at its unit's place so, it is divisible by 5.
iii
1056
The number 1056 has '6' at its unit's place so, it is not divisible by 5.
iv
2735
The number 2735 has '5' at its unit's place so, it is divisible by 5.
v
55053
The number 55053 has '3' at its unit's place so, it is not divisible by 5.
vi
35790
The number 35790 has '0' at its unit's place so, it is divisible by 5.
vii
98765
The number 98765 has '5' at its unit's place so, it is divisible by 5.
viii
42658
The number 42658 has '8' at its unit's place so, it is not divisible by 5.
ix
77990
The number 77990 has '0' at its unit's place so, it is divisible by 5.
Question:9
Test the divisibility of each of the following numbers by 10:
i
205
ii
90
iii
1174
iv
57930
v
60005
Solution:
A given number is divisible by 10 only when its unit digit is 0.
i
205
The number 205 has '5' at its unit's place so, it is not divisible by 10.
ii
90
The number 90 has '0' at its unit's place so, it is divisible by 10.
iii
1174
The number 1174 has '4' at its unit's place so, it is not divisible by 10.
iv
57930
The number 57930 has '0' at its unit's place so, it is divisible by 10.
v
60005
The number 60005 has '5' at its unit's place so, it is not divisible by 10.
Question:10
Test the divisibility of each of the following numers by 3:
i
83
ii
378
iii
474
iv
1693
v
20345
vi
67035
vii
591282
viii
903164
ix
100002
Solution:
A given number is divisible by 3 only when the sum of its digits is divisible by 3.
i
83
Page 3


   
  
    
      
  
      
  
    
Question:7
Test the divisibility of each of the following numers by 2:
i
94
ii
570
iii
285
iv
2398
v
79532
vi
13576
vii
46821
viii
84663
ix
66669
Solution:
A given number is divisible by 2 only when its unit digit is 0, 2, 4, 6 or 8.
i
94
The number 94 has '4' at its unit's place so, it is divisible by 2.
ii
570
The number 570 has '0' at its unit's place so, it is divisible by 2.
iii
285
The number 285 has '5' at its unit's place so, it is not divisible by 2.
iv
2398
The number 2398 has '8' at its unit's place so, it is divisible by 2.
v
79532
The number 79532 has '2' at its unit's place so, it is divisible by 2.
vi
13576
The number 13576 has '6' at its unit's place so, it is divisible by 2.
vii
46821
The number 46821 has '1' at its unit's place so, it is not divisible by 2.
viii
84663
The number 84663 has '3' at its unit's place so, it is not divisible by 2.
ix
66669
The number 66669 has '9' at its unit's place so, it is not divisible by 2.
Question:8
Test the divisibility of each of the following numers by 5:
i
95
ii
470
iii
1056
iv
2735
v
55053
vi
35790
vii
98765
viii
42658
ix
77990
Solution:
A given number is divisible by 5 only when its unit digit is 0 or 5.
i
95
The number 95 has '5' at its unit's place so, it is divisible by 5.
ii
470
The number 470 has '0' at its unit's place so, it is divisible by 5.
iii
1056
The number 1056 has '6' at its unit's place so, it is not divisible by 5.
iv
2735
The number 2735 has '5' at its unit's place so, it is divisible by 5.
v
55053
The number 55053 has '3' at its unit's place so, it is not divisible by 5.
vi
35790
The number 35790 has '0' at its unit's place so, it is divisible by 5.
vii
98765
The number 98765 has '5' at its unit's place so, it is divisible by 5.
viii
42658
The number 42658 has '8' at its unit's place so, it is not divisible by 5.
ix
77990
The number 77990 has '0' at its unit's place so, it is divisible by 5.
Question:9
Test the divisibility of each of the following numbers by 10:
i
205
ii
90
iii
1174
iv
57930
v
60005
Solution:
A given number is divisible by 10 only when its unit digit is 0.
i
205
The number 205 has '5' at its unit's place so, it is not divisible by 10.
ii
90
The number 90 has '0' at its unit's place so, it is divisible by 10.
iii
1174
The number 1174 has '4' at its unit's place so, it is not divisible by 10.
iv
57930
The number 57930 has '0' at its unit's place so, it is divisible by 10.
v
60005
The number 60005 has '5' at its unit's place so, it is not divisible by 10.
Question:10
Test the divisibility of each of the following numers by 3:
i
83
ii
378
iii
474
iv
1693
v
20345
vi
67035
vii
591282
viii
903164
ix
100002
Solution:
A given number is divisible by 3 only when the sum of its digits is divisible by 3.
i
83
The sum of the digits is 8 + 3 = 11 which is not divisible by 3. So, 83 is not divisible by 3.
ii
378
The sum of the digits is 3 + 7 + 8 = 18 which is divisible by 3. So, 378 is divisible by 3.
iii
474
The sum of the digits is 4 + 7 + 4 = 15 which is divisible by 3. So, 474 is divisible by 3.
iv
1693
The sum of the digits is 1 + 6 + 9 + 3 = 19 which is not divisible by 3. So, 1693 is not divisible by 3.
v
20345
The sum of the digits is 2 + 0 + 3 + 4 + 5 = 14 which is not divisible by 3. So, 20345 is not divisible by 3.
vi
67035
The sum of the digits is 6 + 7 + 0 + 3 + 5 = 21 which is divisible by 3. So, 67035 is divisible by 3.
vii
591282
The sum of the digits is 5 + 9 + 1 + 2 + 8 + 2 = 27 which is divisible by 3. So, 591282 is divisible by 3.
viii
903164
The sum of the digits is 9 + 0 + 3 + 1 + 6 + 4 = 23 which is not divisible by 3. So, 903164 is not divisible by 3.
ix
100002
The sum of the digits is 1 + 0 + 0 + 0 + 0 + 2 = 3 which is divisible by 3. So, 100002 is divisible by 3.
Question:11
Test the divisibility of each of the following numbers by 9:
i
327
ii
7524
iii
32022
iv
64302
v
89361
vi
14799
vii
66888
viii
30006
ix
33333
Solution:
A given number is divisible by 9 only when the sum of the digits is divisible by 9.
i
327
The sum of the digits is 3 + 2 + 7 = 12 which is not divisible by 9. So, 327 is not divisible by 9.
ii
7524
The sum of the digits is 7 + 5 + 2 + 4 = 18 which is divisible by 9. So, 7524 is divisible by 9.
iii
32022
The sum of the digits is 3 + 2 + 0 + 2 + 2 = 9 which is divisible by 9. So, 32022 is divisible by 9.
iv
64302
The sum of the digits is 6 + 4 + 3 + 0 + 2 = 15 which is not divisible by 9. So, 64302 is not divisible by 9.
v
89361
The sum of the digits is 8 + 9 + 3 + 6 + 1 = 27 which is divisible by 9. So, 89361 is divisible by 9.
vi
14799
The sum of the digits is 1 + 4 + 7 + 9 + 9 = 30 which is not divisible by 9. So, 14799 is not divisible by 9.
vii
66888
The sum of the digits is 6 + 6 + 8 + 8 + 8 = 36 which is divisible by 9. So, 66888 is divisible by 9.
viii
30006
The sum of the digits is 3 + 0 + 0 + 0 + 6 = 9 which is divisible by 9. So, 30006 is divisible by 9.
ix
33333
The sum of the digits is 3 + 3 + 3 + 3 + 3 = 15 which is not divisible by 9. So, 33333 is not divisible by 9.
Question:12
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Question:7
Test the divisibility of each of the following numers by 2:
i
94
ii
570
iii
285
iv
2398
v
79532
vi
13576
vii
46821
viii
84663
ix
66669
Solution:
A given number is divisible by 2 only when its unit digit is 0, 2, 4, 6 or 8.
i
94
The number 94 has '4' at its unit's place so, it is divisible by 2.
ii
570
The number 570 has '0' at its unit's place so, it is divisible by 2.
iii
285
The number 285 has '5' at its unit's place so, it is not divisible by 2.
iv
2398
The number 2398 has '8' at its unit's place so, it is divisible by 2.
v
79532
The number 79532 has '2' at its unit's place so, it is divisible by 2.
vi
13576
The number 13576 has '6' at its unit's place so, it is divisible by 2.
vii
46821
The number 46821 has '1' at its unit's place so, it is not divisible by 2.
viii
84663
The number 84663 has '3' at its unit's place so, it is not divisible by 2.
ix
66669
The number 66669 has '9' at its unit's place so, it is not divisible by 2.
Question:8
Test the divisibility of each of the following numers by 5:
i
95
ii
470
iii
1056
iv
2735
v
55053
vi
35790
vii
98765
viii
42658
ix
77990
Solution:
A given number is divisible by 5 only when its unit digit is 0 or 5.
i
95
The number 95 has '5' at its unit's place so, it is divisible by 5.
ii
470
The number 470 has '0' at its unit's place so, it is divisible by 5.
iii
1056
The number 1056 has '6' at its unit's place so, it is not divisible by 5.
iv
2735
The number 2735 has '5' at its unit's place so, it is divisible by 5.
v
55053
The number 55053 has '3' at its unit's place so, it is not divisible by 5.
vi
35790
The number 35790 has '0' at its unit's place so, it is divisible by 5.
vii
98765
The number 98765 has '5' at its unit's place so, it is divisible by 5.
viii
42658
The number 42658 has '8' at its unit's place so, it is not divisible by 5.
ix
77990
The number 77990 has '0' at its unit's place so, it is divisible by 5.
Question:9
Test the divisibility of each of the following numbers by 10:
i
205
ii
90
iii
1174
iv
57930
v
60005
Solution:
A given number is divisible by 10 only when its unit digit is 0.
i
205
The number 205 has '5' at its unit's place so, it is not divisible by 10.
ii
90
The number 90 has '0' at its unit's place so, it is divisible by 10.
iii
1174
The number 1174 has '4' at its unit's place so, it is not divisible by 10.
iv
57930
The number 57930 has '0' at its unit's place so, it is divisible by 10.
v
60005
The number 60005 has '5' at its unit's place so, it is not divisible by 10.
Question:10
Test the divisibility of each of the following numers by 3:
i
83
ii
378
iii
474
iv
1693
v
20345
vi
67035
vii
591282
viii
903164
ix
100002
Solution:
A given number is divisible by 3 only when the sum of its digits is divisible by 3.
i
83
The sum of the digits is 8 + 3 = 11 which is not divisible by 3. So, 83 is not divisible by 3.
ii
378
The sum of the digits is 3 + 7 + 8 = 18 which is divisible by 3. So, 378 is divisible by 3.
iii
474
The sum of the digits is 4 + 7 + 4 = 15 which is divisible by 3. So, 474 is divisible by 3.
iv
1693
The sum of the digits is 1 + 6 + 9 + 3 = 19 which is not divisible by 3. So, 1693 is not divisible by 3.
v
20345
The sum of the digits is 2 + 0 + 3 + 4 + 5 = 14 which is not divisible by 3. So, 20345 is not divisible by 3.
vi
67035
The sum of the digits is 6 + 7 + 0 + 3 + 5 = 21 which is divisible by 3. So, 67035 is divisible by 3.
vii
591282
The sum of the digits is 5 + 9 + 1 + 2 + 8 + 2 = 27 which is divisible by 3. So, 591282 is divisible by 3.
viii
903164
The sum of the digits is 9 + 0 + 3 + 1 + 6 + 4 = 23 which is not divisible by 3. So, 903164 is not divisible by 3.
ix
100002
The sum of the digits is 1 + 0 + 0 + 0 + 0 + 2 = 3 which is divisible by 3. So, 100002 is divisible by 3.
Question:11
Test the divisibility of each of the following numbers by 9:
i
327
ii
7524
iii
32022
iv
64302
v
89361
vi
14799
vii
66888
viii
30006
ix
33333
Solution:
A given number is divisible by 9 only when the sum of the digits is divisible by 9.
i
327
The sum of the digits is 3 + 2 + 7 = 12 which is not divisible by 9. So, 327 is not divisible by 9.
ii
7524
The sum of the digits is 7 + 5 + 2 + 4 = 18 which is divisible by 9. So, 7524 is divisible by 9.
iii
32022
The sum of the digits is 3 + 2 + 0 + 2 + 2 = 9 which is divisible by 9. So, 32022 is divisible by 9.
iv
64302
The sum of the digits is 6 + 4 + 3 + 0 + 2 = 15 which is not divisible by 9. So, 64302 is not divisible by 9.
v
89361
The sum of the digits is 8 + 9 + 3 + 6 + 1 = 27 which is divisible by 9. So, 89361 is divisible by 9.
vi
14799
The sum of the digits is 1 + 4 + 7 + 9 + 9 = 30 which is not divisible by 9. So, 14799 is not divisible by 9.
vii
66888
The sum of the digits is 6 + 6 + 8 + 8 + 8 = 36 which is divisible by 9. So, 66888 is divisible by 9.
viii
30006
The sum of the digits is 3 + 0 + 0 + 0 + 6 = 9 which is divisible by 9. So, 30006 is divisible by 9.
ix
33333
The sum of the digits is 3 + 3 + 3 + 3 + 3 = 15 which is not divisible by 9. So, 33333 is not divisible by 9.
Question:12
Test the divisibility of each of the following numbers by 8:
i
134
ii
618
iii
3928
iv
50176
v
39392
vi
56794
vii
86102
viii
66666
ix
99918
x
77736
Solution:
A given number is divisible by 4 only when the number formed by its last two digits is divisible by 4.
i
134
The last two digits of 134 are '34' which is not divisible by 4. Hence, 134 is not divisible by 4.
ii
618
The last two digits of 618 are '18' which is not divisible by 4. Hence, 618 is not divisible by 4.
iii
3928
The last two digits of 3928 are '28' which is divisible by 4. Hence, 3928 is divisible by 4.
iv
50176
The last two digits of 50176 are '76' which is divisible by 4. Hence, 50176 is divisible by 4.
v
39392
The last two digits of 39392 are '92' which is divisible by 4. Hence, 39392 is divisible by 4.
vi
56794
The last two digits of 56794 are '94' which is not divisible by 4. Hence, 56794 is not divisible by 4.
vii
86102
The last two digits of 86102 are '02' which is not divisible by 4. Hence, 86102 is not divisible by 4.
viii
66666
The last two digits of 66666 are '66' which is not divisible by 4. Hence, 66666 is not divisible by 4.
ix
99918
The last two digits of 99918 are '18' which is not divisible by 4. Hence, 99918 is not divisible by 4.
x
77736
The last two digits of 77736 are '36' which is divisible by 4. Hence, 77736 is divisible by 4.
 
Question:13
Text the divisibility of each of the following numbers by 5:
i
95
ii
470
iii
1056
iv
2735
v
55053
vi
35790
vii
98765
viii
42658
ix
77990
Solution:
A number is divisible by 8 only when the number formed by its last three digits is divisible by 8.
i
6132
The last three digits of the given number are 132 which is not divisible by 8. So, 6132 is not divisible by 8.
ii
7304
Page 5


   
  
    
      
  
      
  
    
Question:7
Test the divisibility of each of the following numers by 2:
i
94
ii
570
iii
285
iv
2398
v
79532
vi
13576
vii
46821
viii
84663
ix
66669
Solution:
A given number is divisible by 2 only when its unit digit is 0, 2, 4, 6 or 8.
i
94
The number 94 has '4' at its unit's place so, it is divisible by 2.
ii
570
The number 570 has '0' at its unit's place so, it is divisible by 2.
iii
285
The number 285 has '5' at its unit's place so, it is not divisible by 2.
iv
2398
The number 2398 has '8' at its unit's place so, it is divisible by 2.
v
79532
The number 79532 has '2' at its unit's place so, it is divisible by 2.
vi
13576
The number 13576 has '6' at its unit's place so, it is divisible by 2.
vii
46821
The number 46821 has '1' at its unit's place so, it is not divisible by 2.
viii
84663
The number 84663 has '3' at its unit's place so, it is not divisible by 2.
ix
66669
The number 66669 has '9' at its unit's place so, it is not divisible by 2.
Question:8
Test the divisibility of each of the following numers by 5:
i
95
ii
470
iii
1056
iv
2735
v
55053
vi
35790
vii
98765
viii
42658
ix
77990
Solution:
A given number is divisible by 5 only when its unit digit is 0 or 5.
i
95
The number 95 has '5' at its unit's place so, it is divisible by 5.
ii
470
The number 470 has '0' at its unit's place so, it is divisible by 5.
iii
1056
The number 1056 has '6' at its unit's place so, it is not divisible by 5.
iv
2735
The number 2735 has '5' at its unit's place so, it is divisible by 5.
v
55053
The number 55053 has '3' at its unit's place so, it is not divisible by 5.
vi
35790
The number 35790 has '0' at its unit's place so, it is divisible by 5.
vii
98765
The number 98765 has '5' at its unit's place so, it is divisible by 5.
viii
42658
The number 42658 has '8' at its unit's place so, it is not divisible by 5.
ix
77990
The number 77990 has '0' at its unit's place so, it is divisible by 5.
Question:9
Test the divisibility of each of the following numbers by 10:
i
205
ii
90
iii
1174
iv
57930
v
60005
Solution:
A given number is divisible by 10 only when its unit digit is 0.
i
205
The number 205 has '5' at its unit's place so, it is not divisible by 10.
ii
90
The number 90 has '0' at its unit's place so, it is divisible by 10.
iii
1174
The number 1174 has '4' at its unit's place so, it is not divisible by 10.
iv
57930
The number 57930 has '0' at its unit's place so, it is divisible by 10.
v
60005
The number 60005 has '5' at its unit's place so, it is not divisible by 10.
Question:10
Test the divisibility of each of the following numers by 3:
i
83
ii
378
iii
474
iv
1693
v
20345
vi
67035
vii
591282
viii
903164
ix
100002
Solution:
A given number is divisible by 3 only when the sum of its digits is divisible by 3.
i
83
The sum of the digits is 8 + 3 = 11 which is not divisible by 3. So, 83 is not divisible by 3.
ii
378
The sum of the digits is 3 + 7 + 8 = 18 which is divisible by 3. So, 378 is divisible by 3.
iii
474
The sum of the digits is 4 + 7 + 4 = 15 which is divisible by 3. So, 474 is divisible by 3.
iv
1693
The sum of the digits is 1 + 6 + 9 + 3 = 19 which is not divisible by 3. So, 1693 is not divisible by 3.
v
20345
The sum of the digits is 2 + 0 + 3 + 4 + 5 = 14 which is not divisible by 3. So, 20345 is not divisible by 3.
vi
67035
The sum of the digits is 6 + 7 + 0 + 3 + 5 = 21 which is divisible by 3. So, 67035 is divisible by 3.
vii
591282
The sum of the digits is 5 + 9 + 1 + 2 + 8 + 2 = 27 which is divisible by 3. So, 591282 is divisible by 3.
viii
903164
The sum of the digits is 9 + 0 + 3 + 1 + 6 + 4 = 23 which is not divisible by 3. So, 903164 is not divisible by 3.
ix
100002
The sum of the digits is 1 + 0 + 0 + 0 + 0 + 2 = 3 which is divisible by 3. So, 100002 is divisible by 3.
Question:11
Test the divisibility of each of the following numbers by 9:
i
327
ii
7524
iii
32022
iv
64302
v
89361
vi
14799
vii
66888
viii
30006
ix
33333
Solution:
A given number is divisible by 9 only when the sum of the digits is divisible by 9.
i
327
The sum of the digits is 3 + 2 + 7 = 12 which is not divisible by 9. So, 327 is not divisible by 9.
ii
7524
The sum of the digits is 7 + 5 + 2 + 4 = 18 which is divisible by 9. So, 7524 is divisible by 9.
iii
32022
The sum of the digits is 3 + 2 + 0 + 2 + 2 = 9 which is divisible by 9. So, 32022 is divisible by 9.
iv
64302
The sum of the digits is 6 + 4 + 3 + 0 + 2 = 15 which is not divisible by 9. So, 64302 is not divisible by 9.
v
89361
The sum of the digits is 8 + 9 + 3 + 6 + 1 = 27 which is divisible by 9. So, 89361 is divisible by 9.
vi
14799
The sum of the digits is 1 + 4 + 7 + 9 + 9 = 30 which is not divisible by 9. So, 14799 is not divisible by 9.
vii
66888
The sum of the digits is 6 + 6 + 8 + 8 + 8 = 36 which is divisible by 9. So, 66888 is divisible by 9.
viii
30006
The sum of the digits is 3 + 0 + 0 + 0 + 6 = 9 which is divisible by 9. So, 30006 is divisible by 9.
ix
33333
The sum of the digits is 3 + 3 + 3 + 3 + 3 = 15 which is not divisible by 9. So, 33333 is not divisible by 9.
Question:12
Test the divisibility of each of the following numbers by 8:
i
134
ii
618
iii
3928
iv
50176
v
39392
vi
56794
vii
86102
viii
66666
ix
99918
x
77736
Solution:
A given number is divisible by 4 only when the number formed by its last two digits is divisible by 4.
i
134
The last two digits of 134 are '34' which is not divisible by 4. Hence, 134 is not divisible by 4.
ii
618
The last two digits of 618 are '18' which is not divisible by 4. Hence, 618 is not divisible by 4.
iii
3928
The last two digits of 3928 are '28' which is divisible by 4. Hence, 3928 is divisible by 4.
iv
50176
The last two digits of 50176 are '76' which is divisible by 4. Hence, 50176 is divisible by 4.
v
39392
The last two digits of 39392 are '92' which is divisible by 4. Hence, 39392 is divisible by 4.
vi
56794
The last two digits of 56794 are '94' which is not divisible by 4. Hence, 56794 is not divisible by 4.
vii
86102
The last two digits of 86102 are '02' which is not divisible by 4. Hence, 86102 is not divisible by 4.
viii
66666
The last two digits of 66666 are '66' which is not divisible by 4. Hence, 66666 is not divisible by 4.
ix
99918
The last two digits of 99918 are '18' which is not divisible by 4. Hence, 99918 is not divisible by 4.
x
77736
The last two digits of 77736 are '36' which is divisible by 4. Hence, 77736 is divisible by 4.
 
Question:13
Text the divisibility of each of the following numbers by 5:
i
95
ii
470
iii
1056
iv
2735
v
55053
vi
35790
vii
98765
viii
42658
ix
77990
Solution:
A number is divisible by 8 only when the number formed by its last three digits is divisible by 8.
i
6132
The last three digits of the given number are 132 which is not divisible by 8. So, 6132 is not divisible by 8.
ii
7304
The last three digits of the given number are 304 which is divisible by 8. So, 7304 is divisible by 8.
iii
59312
The last three digits of the given number are 312 which is divisible by 8. So, 59312 is divisible by 8.
iv
66664
The last three digits of the given number are 664 which is divisible by 8. So, 66664 is divisible by 8.
v
44444
The last three digits of the given number are 444 which is not divisible by 8. So, 44444 is not divisible by 8.
vi
154360
The last three digits of the given number are 360 which is divisible by 8. So, 154360 is divisible by 8.
vii
998818
The last three digits of the given number are 818 which is not divisible by 8. So, 998818 is not divisible by 8.
viii
265472
The last three digits of the given number are 472 which is divisible by 8. So, 265472 is divisible by 8.
ix
7350162
The last three digits of the given number are 162 which is not divisible by 8. So, 7350162 is not divisible by 8.
Question:14
Test the divisibility of each of the following numbers by 11:
i
22222
ii
444444
iii
379654
iv
1057982
v
6543207
vi
818532
vii
900163
viii
7531622
Solution:
A given number is divisible by 11, if the difference between the sum of its digits at odd places and the sum of its digits at even places is
either 0 or a number divisible by 11.
i
22222
For the given number,
sum of the digits at odd places = 2 + 2 + 2 = 6
sum of digits at even places = 2 + 2 = 4
Difference of the above sums = 6 - 4 = 2
Since the difference is not 0 and neither a number divisible by 11 so, the 22222 is not divisible by 11.
ii
444444
For the given number,
sum of the digits at odd places = 4 + 4 + 4 = 12
sum of digits at even places = 4 + 4 + 4 = 12
Difference of the above sums = 12 - 12 = 0
Since the difference is 0 so the given number 444444 is divisible by 11.
iii
379654
For the given number,
sum of the digits at odd places = 4 + 6 + 7 = 17
sum of digits at even places = 5 + 9 + 3 = 17
Difference of the above sums = 17 - 17 = 0
Since the difference is 0 so the given number 379654 is divisible by 11.
iv
1057982
For the given number,
sum of the digits at odd places = 2 + 9 + 5 + 1 = 17
sum of digits at even places = 8 + 7 + 0 = 15
Difference of the above sums = 17 - 15= 2
Since the difference is not 0 and neither a number divisible by 11 so, the 1057982 is not divisible by 11.
v
6543207
For the given number,
sum of the digits at odd places = 7 + 2 + 4 + 6 = 19
sum of digits at even places = 0 + 3 + 5 = 8
Difference of the above sums = 19 - 8 = 11
Since the difference is 11 which is surely divisible by 11 so the given number 6543207 is divisible by 11.
vi
818532
For the given number,