Questions and Solutions for NCERT Class 6th Mathematics Chapter 3 – Playing with Numbers – Exercise 3.3
1. Using divisibility tests, determine which of the following numbers are divisible by 2; by 3; by 4; by 5; by 6; by 8; by 9; by 10 ; by 11 (say, yes or no):
(a)128 is divisible by 2, 4 and 8
(b)990 is divisible by 2, 3, 5, 6, 9, 10 and 11
(c)1586 is divisible by 2
(d)275 is divisible by 5 and 11
(e)6686 is divisible by 2
(f)639210 is divisible by 2, 3, 5, 6, 10 and 11
(g)429714 is divisible by 2, 3, 6 and 9
(h)2856 is divisible by 2, 3, 4, 6 and 8
(i)3060 is divisible by 2, 3, 4, 5, 6, 9 and 10
(j)406839 is divisible by 3
2. Using divisibility tests, determine which of the following numbers are divisible by 4; by 8:
(a) 572
Ans: Since the last two digits are divisible by 4 the number is divisible by 4
Since the last three digits are not divisible by 8 the number is not divisible by 8
(b) 726352
Ans: Since the last two digits are divisible by 4 the number is divisible by 4
Since the last three digits are divisible by 8 the number is divisible by 8
(c) 5500
Ans: Since the last two digits are divisible by 4 the number is divisible by 4
Since the last three digits are not divisible by 8 the number is not divisible by 8
(d) 6000
Ans: Since the last two digits are divisible by 4 the number is divisible by 4
Since the last three digits are divisible by 8 the number is divisible by 8
(e) 12159
Ans: Since the last two digits are not divisible by 4 the number is not divisible by 4
Since the last three digits are not divisible by 8 the number is not divisible by 8
Also the number is an odd number so it is not divisible by 4 and 8
(f) 14560
Ans: Since the last two digits are divisible by 4 the number is divisible by 4
Since the last three digits are divisible by 8 the number is divisible by 8
(g) 21084
Ans: Since the last two digits are divisible by 4 the number is divisible by 4
Since the last three digits are not divisible by 8 the number is not divisible by 8
(h) 31795072
Ans: Since the last two digits are divisible by 4 the number is divisible by 4
Since the last three digits are divisible by 8 the number is divisible by 8
(i) 1700
Ans: Since the last two digits are divisible by 4 the number is divisible by 4
Since the last three digits are not divisible by 8 the number is not divisible by 8
(j) 2150
Ans: Since the last two digits are not divisible by 4 the number is not divisible by 4
Since the last three digits are not divisible by 8 the number is not divisible by 8
3. Using divisibility tests, determine which of following numbers are divisible by 6:
(a) 297144
Ans: The number is divisible by 2 as its unit digit is an even number
The number is divisible by three as the sum (27) of its digit is divisible by 3
Since the number is divisible by both 2 and 3, therefore it is also divisible by 6
(b) 1258
Ans: The number is divisible by 2 as its unit digit is an even number
The number is not divisible by three as the sum (16) of its digit is not divisible by 3
Since the number is not divisible by both 2 and 3, therefore it is not divisible by 6
(c) 4335
Ans: The number is not divisible by 2 as its unit digit is an odd number
The number is divisible by three as the sum (15) of its digit is divisible by 3
Since the number is not divisible by both 2 and 3, therefore it is not divisible by 6
(d) 61233
Ans: The number is not divisible by 2 as its unit digit is an odd number
The number is divisible by three as the sum (15) of its digit is divisible by 3
Since the number is not divisible by both 2 and 3, therefore it is not divisible by 6
(e) 901352
Ans: The number is divisible by 2 as its unit digit is an even number
The number is not divisible by three as the sum (20) of its digit is not divisible by 3
Since the number is not divisible by both 2 and 3, therefore it is not divisible by 6
(f) 438750
Ans: The number is divisible by 2 as its unit digit is an even number
The number is divisible by three as the sum (27) of its digit is divisible by 3
Since the number is divisible by both 2 and 3, therefore it is also divisible by 6
(g) 1790184
Ans: The number is divisible by 2 as its unit digit is an even number
The number is not divisible by three as the sum (30) of its digit is not divisible by 3
Since the number is not divisible by both 2 and 3, therefore it is not divisible by 6
(h) 12583
Ans: The number is not divisible by 2 as its unit digit is an odd number
The number is not divisible by three as the sum (19) of its digit is not divisible by 3
Since the number is not divisible by both 2 and 3, therefore it is not divisible by 6
(i) 639210
Ans: The number is divisible by 2 as its unit digit is an even number
The number is divisible by three as the sum (21) of its digit is divisible by 3
Since the number is divisible by both 2 and 3, therefore it is also divisible by 6
(j) 17852
Ans: The number is divisible by 2 as its unit digit is an even number
The number is not divisible by three as the sum (23) of its digit is not divisible by 3
Since the number is not divisible by both 2 and 3, therefore it is not divisible by 6
4. Using divisibility tests, determine which of the following numbers are divisible by 11:
(a) 5445
Ans: Sum of digits at odd places = 4+5 = 9
Sum of digits at even places = 4 + 5 = 9
Difference of both sums = 9 – 9 = 0
Since the difference is 0, therefore the number is divisible by 11
(b) 10824
Ans: Sum of digits at odd places = 1 + 8 + 4 = 13
Sum of digits at even places = 0 + 2 = 2
Difference of both sums = 13 – 2 = 11
Since the difference is 11, therefore the number is divisible by 11
(c) 7138965
Ans: Sum of digits at odd places = 7 + 3 + 9 +5 = 24
Sum of digits at even places = 1 + 8 + 6 = 15
Difference of both sums = 24 – 15 = 9
Since the difference is neither 0 nor 11, therefore the number is not divisible by 11
(d) 70169308
Ans: Sum of digits at odd places = 0 + 6 +3 +8 = 17
Sum of digits at even places = 7 + 1 + 9 + 0 =17
Difference of both sums = 17 – 17 = 0
Since the difference is 0, therefore the number is divisible by 11
(e) 10000001
Ans: Sum of digits at odd places = 0 + 0 + 0 + 1 = 1
Sum of digits at even places = 1 + 0 + 0 + 0 = 1
Difference of both sums = 1 – 1 = 0
Since the difference is 0, therefore the number is divisible by 11
(f) 901153
Ans: Sum of digits at odd places = 0 + 1 + 3 = 4
Sum of digits at even places = 9 + 1 + 5 = 15
Difference of both sums = 15 – 4 = 11
Since the difference is 11, therefore the number is divisible by 11
5. Write the smallest digit and the greatest digit in the blank space of each of the following numbers so that the number formed is divisible by 3 :
(a) __ 6724
Sol: We know that a number is divisible by three if the sum of its digits is divisible by 3
Smallest digit = 2 = 2 + 6 + 7 + 2 + 4 = 21
Greatest digit = 8 = 8 + 6 + 7 + 2 + 4 = 27
(b) 4765 __ 2
Sol: We know that a number is divisible by three if the sum of its digits is divisible by 3
Smallest digit = 0 = 4 + 7 + 6 + 5 + 0 + 2 = 24
Greatest digit = 9 = 4 + 7 + 6 + 5 + 9 + 2 = 33
6. Write a digit in the blank space of each of the following numbers so that the number formed is divisible by 11 :
(a) 92 __ 389
Sol: We know that, if the difference between the sum of the digits at odd places (from the right) and the sum of the digits at even places (from the right) of the number is either 0 or 11, then the number is divisible by 11.
928389
Sum of digits at Odd places = 9+3+2=14
Sum of digits at Even places = 9+8+8=25
Difference = 25 – 14 = 11
(b) 8 __ 9484
Sol: We know that, if the difference between the sum of the digits at odd places (from the right) and the sum of the digits at even places (from the right) of the number is either 0 or 11, then the number is divisible by 11.
869484
Sum of digits at Odd places = 6+4+4=14
Sum of digits at Even places = 8+9+8=25
Difference = 25 – 14 = 11
You can find the solutions for Class 6 Mathematics previous exercises from here
- Playing with Numbers – Exercise 3.2 Solutions
- Playing with Numbers – Exercise 3.1 Solutions
- Whole Numbers – Exercise 2.3 Solutions
- Whole Numbers – Exercise 2.2 Solutions
- Whole Numbers – Exercise 2.1 Solutions
- Knowing Our Numbers Solutions Exercise 1.3 Solutions
- Knowing Our Numbers Solutions Exercise 1.2 Solutions
- Knowing Our Numbers Solutions Exercise 1.1 Solutions
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