Selina Solutions Concise Mathematics Class 6 Chapter 9 Playing With Numbers Exercise 9(C) provides basic fundamental concepts on the divisibility of numbers covered under this exercise. Students gain better conceptual knowledge by practising these solutions effectively. They can solve difficult questions by referring to solutions PDF and hence, also boost their confidence. Those who desire to score well in exams need to practice Selina Solutions created by experts, as per the ICSE guidelines. Download the Selina Solutions Concise Mathematics Class 6 Chapter 9 Playing With Numbers Exercise 9(C) PDF, from the links provided below
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Exercise 9(A) Solutions
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Access Selina Solutions Concise Mathematics Class 6 Chapter 9 Playing With Numbers Exercise 9(C)
Exercise 9(C)
1. Find which of the following numbers are divisible by 2:
(i) 352
(ii) 523
(iii) 496
(iv) 649
Solution:
(i) 352
The given number = 352
Digit at unit’s place = 2
Hence, the number is divisible by 2
(ii) 523
The given number = 523
Digit at unit’s place = 3
Hence, the number is not divisible by 2
(iii) 496
The given number = 496
Digit at unit’s place = 6
Hence, the number is divisible by 2
(iv) 649
The given number = 649
Digit at unit’s place = 9
Hence, the number is not divisible by 2
2. Find which of the following number are divisible by 4:
(i) 222
(ii) 532
(iii) 678
(iv) 9232
Solution:
(i) 222
The given number = 222
The number formed by ten’s and unit digit is 22, which is not divisible by 4.
Hence, the number is not divisible by 4
(ii) 532
The given number = 532
The number formed by ten’s and unit digit is 32, which is divisible by 4.
Hence, the number is divisible by 4
(iii) 678
The given number = 678
The number formed by ten’s and unit digit is 78, which is not divisible by 4
Hence, the number is not divisible by 4
(iv) 9232
The given number = 9232
The number formed by ten’s and unit digit is 32, which is divisible by 4
Hence, the number is divisible by 4
3. Find which of the following numbers are divisible by 8:
(i) 324
(ii) 2536
(iii) 92760
(iv) 444320
Solution:
(i) 324
The given number = 324
The number formed by hundred’s, ten’s and unit digit is 324, which is not divisible by 8
Hence, 324 is not divisible by 8
(ii) 2536
The given number = 2536
The number formed by hundred’s, ten’s and unit digit is 536, which is divisible by 8
Hence, 2536 is divisible by 8
(iii) 92760
The given number = 92760
The number formed by hundred’s, ten’s and unit digit is 760, which is divisible by 8
Hence, 92760 is divisible by 8
(iv) 444320
The given number = 444320
The number formed by hundred’s, ten’s and unit digit is 320, which is divisible by 8
Hence, 444320 is divisible by 8
4. Find which of the following numbers are divisible by 3:
(i) 221
(ii) 543
(iii) 28492
(iv) 92349
Solution:
(i) 221
The given number = 221
For a number to be divisible by 3, sum of digits must be divisible by 3
Sum of digits = 2 + 2 + 1 = 5
Since 5 is not divisible by 3
Hence, 221 is not divisible by 3
(ii) 543
The given number = 543
For a number to be divisible by 3, sum of digits must be divisible by 3
Sum of digits = 5 + 4 + 3 = 12
Since 12 is divisible by 3
Hence, 543 is divisible by 3
(iii) 28492
The given number = 28492
For a number to be divisible by 3, sum of digits must be divisible by 3
Sum of digits = 2 + 8 + 4 + 9 + 2 = 25
Since 25 is not divisible by 3
Hence, 28492 is not divisible by 3
(iv) 92349
The given number = 92349
For a number to be divisible by 3, sum of digits must be divisible by 3
Sum of digits = 9 + 2 + 3 + 4 + 9 = 27
Since 27 is divisible by 3
Hence, 92349 is divisible by 3
5. Find which of the following numbers are divisible by 9:
(i) 1332
(ii) 53247
(iii) 4968
(iv) 200314
Solution:
(i) 1332
The given number = 1332
For a number to be divisible by 9, sum of digits must be divisible by 9
Sum of digits = 1 + 3 + 3 + 2 = 9
Since 9 is divisible by 9
Hence, 1332 is divisible by 9
(ii) 53247
The given number = 53247
For a number to be divisible by 9, sum of digits must be divisible by 9
Sum of digits = 5 + 3 + 2 + 4 + 7 = 21
Since 21 is not divisible by 9
Hence, 53247 is not divisible by 9
(iii) 4968
The given number = 4968
For a number to be divisible by 9, sum of digits must be divisible by 9
Sum of digits = 4 + 9 + 6 + 8 = 27
Since 27 is divisible by 9
Hence, 4968 is divisible by 9
(iv) 200314
The given number = 200314
For a number to be divisible by 9, sum of digits must be divisible by 9
Sum of digits = 2 + 0 + 0 + 3 + 1 + 4 = 10
Since 10 is not divisible by 9
Hence, 200314 is not divisible by 9
6. Find which of the following number are divisible by 6:
(i) 324
(ii) 2010
(iii) 33278
(iv) 15505
Solution:
A number which is divisible by either 2 and 3 or both then the given number is divisible by 6
(i) 324
The given number = 324
Sum of digits = 3 + 2 + 4 = 9
which is divisible by 3
Therefore, 324 is divisible by 6
(ii) 2010
The given number = 2010
Sum of digits = 2 + 0 + 1 + 0 = 3
which is divisible by 3
Therefore, 2010 is divisible by 6
(iii) 33278
The given number = 33278
Sum of digits = 3 + 3 + 2 + 7 + 8 = 23
Unit digit is 3, which is odd
Therefore, 33278 is not divisible by 6
(iv) 15505
The given number = 15505
Sum of digits = 1 + 5 + 5 + 0 + 5 = 16
which is divisible by 2
Therefore, 15505 is divisible by 6
7. Find which of the following numbers are divisible by 5:
(i) 5080
(ii) 66666
(iii) 755
(iv) 9207
Solution:
(i) 5080
The given number = 5080
For a number to be divisible by 5, units digit must be 0 or 5
Here, unit digit is 0
Therefore, 5080 is divisible by 5
(ii) 66666
The given number = 66666
For a number to be divisible by 5, units digit must be 0 or 5
Here, unit digit is 6
Therefore, 66666 is not divisible by 5
(iii) 755
The given number = 755
For a number to be divisible by 5, units digit must be 0 or 5
Here, unit digit is 5
Therefore, 755 is divisible by 5
(iv) 9207
The given number = 9207
For a number to be divisible by 5, units digit must be 0 or 5
Here, unit digit is 7
Therefore, 9207 is not divisible by 5
8. Find which of the following numbers are divisible by 10:
(i) 9990
(ii) 0
(iii) 847
(iv) 8976
Solution:
(i) 9990
The given number = 9990
For a number to be divisible by 10, unit’s digit must be 0
Here, unit digit is 0
Therefore, 9990 is divisible by 10
(ii) 0
The given number = 0
For a number to be divisible by 10, unit’s digit must be 0
Here, unit digit is 0
Therefore, 0 is divisible by 10
(iii) 847
The given number = 847
For a number to be divisible by 10, unit’s digit must be 0
Here, unit digit is 7
Therefore, 847 is not divisible by 10
(iv) 8976
The given number = 8976
For a number to be divisible by 10, unit’s digit must be 0
Here, unit digit is 6
Therefore, 8976 is not divisible by 10
9. Find which of the following numbers are divisible by 11:
(i) 5918
(ii) 68,717
(iii) 3882
(iv) 10857
Solution:
(i) 5918
The given number = 5918
If the difference of sum of its digit in odd places from left side and sum of digits in even places from left side is divisible by 11 then the number is divisible by 11
Sum of digits at odd places = 5 + 1 = 6
Sum of digits at even places = 9 + 8 = 17
Difference = 17 – 6 = 11
Here, the difference is 11 which is divisible by 11
Hence, the number is divisible by 11
(ii) 68717
The given number = 68717
If the difference of sum of its digit in odd places from left side and sum of digits in even places from left side is divisible by 11 then the number is divisible by 11
Sum of digits at odd places = 6 + 7 + 7 = 20
Sum of digits at even places = 8 + 1 = 9
Difference = 20 – 9 = 11
Here, difference is 11 which is divisible by 11
Hence, the number is divisible by 11
(iii) 3882
The given number = 3882
If the difference of sum of its digit in odd places from left side and sum of digits in even places from left side is divisible by 11 then the number is divisible by 11
Sum of digits at odd places = 3 + 8 = 11
Sum of digits at even places = 8 + 2 = 10
Difference = 11 – 10 = 1
Here, difference is 1 which is not divisible by 11
Hence, the number is not divisible by 11
(iv) 10857
The given number = 10857
If the difference of sum of its digit in odd places from left side and sum of digits in even places from left side is divisible by 11 then the number is divisible by 11
Sum of digits at odd places = 1 + 8 + 7 = 16
Sum of digits at even places = 0 + 5 = 5
Difference = 16 – 5 = 11
Here, difference is 11which is divisible by 11
Hence, the number is divisible by 11
10. Find which of the following numbers are divisible by 15:
(i) 960
(ii) 8295
(iii) 10243
(iv) 5013
Solution:
(i) 960
The given number = 960
For a number to be divisible by 15, it should be divisible by both 3 and 5
Sum of digits = 9 + 6 + 0 = 15
Since 15 is divisible by 3
So, the number is divisible by 3
Here, unit digit is 0, so it is divisible by 5
Hence, the number is divisible by 15
(ii) 8295
The given number = 8295
For a number to be divisible by 15 it should be divisible by both 3 and 5
Sum of digits = 8 + 2 + 9 + 5 = 24
Since 24 is divisible by 3
So, the number is divisible by 3
Here, unit digit is 5, so it is divisible by 5
Hence, the number is divisible by 15
(iii) 10243
The given number = 10243
For a number to be divisible by 15 it should be divisible by both 3 and 5
Sum of digits = 1 + 0 + 2 + 4 + 3 = 10
Since 10 is not divisible by 3
So, the number is not divisible by 3
Here, unit digit is 3, so it is not divisible by 5
Hence, the number is not divisible by 15
(iv) 5013
The given number = 5013
For a number to be divisible by 15 it should be divisible by both 3 and 5
Sum of digits = 5 + 0 + 1 + 3 = 9
Since 9 is divisible by 3
So, the number is divisible by 3
Here, unit digit is 3, so it is not divisible by 5
Hence, the number is not divisible by 15
11. In each of the following numbers, replace M by the smallest number to make resulting number divisible by 3:
(i) 64 M 3
(ii) 46 M 46
(iii) 27 M 53
Solution:
(i) 64 M 3
The given number = 64 M 3
For a number to be divisible by 3 sum of digits must be divisible by 3
Sum of digits = 6 + 4 + 3 = 13
The number which is divisible by 3 next to 13 is 15
Required smallest number = 15 – 13 = 2
Hence, value of M is 2
(ii) 46 M 46
The given number = 46 M 46
For a number to be divisible by 3 sum of digits must be divisible by 3
Sum of digits = 4 + 6 + 4 + 6 = 20
The number which is divisible by 3 next to 20 is 21
Required smallest number = 21 – 20 = 1
Hence, the value of M is 1
(iii) 27 M 53
The given number = 27 M 53
For a number to be divisible by 3 sum of digits must be divisible by 3
Sum of digits = 2 + 7 + 5 + 3 = 17
The number which is divisible by 3 next to 17 is 18
Required smallest number = 18 – 17 = 1
Hence, the value of M is 1
12. In each of the following numbers replace M by the smallest number to make resulting number divisible by 9
(i) 76 M 91
(ii) 77548 M
(iii) 627 M 9
Solution:
(i) 76 M 91
The given number is 76 M 91
For a number to be divisible by 9 sum of digits must be divisible by 9
Sum of digits = 7 + 6 + 9 + 1 = 23
The number which is divisible by 9 next to 23 is 27
Required smallest number = 27 – 23 = 4
Hence, the value of M is 4
(ii) 77548 M
The given number = 77548 M
For a number to be divisible by 9 sum of digits must be divisible by 9
Sum of digits = 7 + 7 + 5 + 4 + 8 = 31
The number which is divisible by 9 next to 31 is 36
Required smallest number = 36 – 31 = 5
Hence, the value of M is 5
(iii) 627 M 9
The given number = 627 M 9
For a number to be divisible by 9 sum of digits must be divisible by 9
Sum of digits = 6 + 2 + 7 + 9 = 24
The number which is divisible by 9 next to 24 is 27
Required smallest number = 27 – 24 = 3
Hence, the value of M is 3
13. In each of the following numbers, replace M by the smallest number to make resulting number divisible by 11
(i) 39 M 2
(ii) 3 M 422
(iii) 70975 M
(iv) 14 M 75
Solution:
(i) 39 M 2
The given number = 39 M 2
A number is divisible by 11, if the difference of sum of its digit in odd places from left side and sum of digits in even places from left side is divisible by 11
Sum of its digits in odd places = 3 + M
Sum of its digits in even places = 9 + 2 = 11
Difference:
11 – (3 + M) = 0
11 – 3 – M = 0
8 – M = 0
M = 8
Hence, the value of M is 8
(ii) 3 M 422
The given number = 3 M 422
A number is divisible by 11, if the difference of sum of its digit in odd places from left side and sum of digits in even places from left side is divisible by 11
Sum of its digits in odd places = 3 + 4 + 2 = 9
Sum of its digits in even places = M + 2 = 11
Difference:
9 – (M + 2) = 0
9 – M – 2 = 0
9 – M = 2
M = 7
Hence, the value of M is 7
(iii) 70975 M
The given number is 70975 M
A number is divisible by 11, if the difference of sum of its digit in odd places from left side and sum of digits in even places from left side is divisible by 11
Sum of its digits in odd places = 7 + 9 + 5 = 21
Sum of its digits in even places = 0 + 7 + M = 7 + M
Difference:
21 – (7 + M) = 0
21 = 7 + M
M = 14
Hence, the value of M is 14
(iv) 14 M 75
The given number is 14 M 75
A number is divisible by 11, if the difference of sum of its digit in odd places from left side and sum of digits in even places from left side is divisible by 11
Sum of its digits in odd places = 1 + M + 5
= 6 + M
Sum of its digits in even places = 4 + 7
= 11
Difference:
11 – (6 + M) = 0
11 = 6 + M
M = 11 – 6
M = 5
Hence, the value of M is 5
14. State, true or false:
(i) If a number is divisible by 4. It is divisible by 8
(ii) If a number is a factor 16 and 24, it is a factor of 48
(iii) If a number is divisible by 18, it is divisible by 3 and 6
(iv) If a divide b and c completely, then a divides (i) a + b (ii) a – b also completely.
Solution:
(i) False
The number is divisible by 4, if tens and unit digit is divisible by 4
The number is divisible by 8, if hundreds, tens and unit digit is divisible by 8
(ii) True
As 16 and 24 are factors of 48
(iii) True
The product of 3 and 6 is 18, so if a number is divisible by 18, it is divisible by 3 and 6
(iv) True
If a divides b and c completely, then a divides a + b and a – b completely
Hence, if a number is a factor of each of the two numbers, then it is a factor of their sum also
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