Class 6 maths Exercise 3.3 solutions
NCERT mathematics class 6 chapter 3 Playing with Numbers exercise 3.3 solutions are given.
You should study the textbook lesson Playing with Numbers very well.
You should also observe and practice all example problems and solutions given in the textbook.
observe the solutions given below and try them in your own method.
NCERT maths class 6 solutions
Exercise 3.1
Exercise 3.2
Exercise 3.3
Exercise 3.4
Exercise 3.5
Exercise 3.6
Exercise 3.7
Chapter 3 exercise 3.3 solutions Playing with Numbers class 6 maths NCERT
Std 6 maths textbook solutions
Chapter 3
Playing with Numbers
Exercise 3.3
NCERT class 6 maths chapter 3 exercise 3.3 Playing with Numbers
Problem 1
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.
a. 128, b. 990, c. 1586, d. 275, e. 6686, f. 639210, g. 429714, h. 2856, i. 3060, j. 406839
Solutions:
a. 128
128 is divisible by 2, 4, 8.
128 is not divisible by 3, 5, 6, 9, 10, 11.
b. 990
990 is divisible by 2, 3, 5, 6, 9, 10, 11.
990 is not divisible by 4, 8
c. 1586
1586 is divisible by 2
1586 is not divisible by 3, 4, 5, 6, 8, 9, 10, 11
d. 275
275 is divisible by 5, 11
275 is not divisible by 2, 3, 4, 6, 8, 9, 10
e. 6686
6686 is divisible by 2
6686 is not divisible by 3, 4, 5, 6, 8, 9, 10, 11
f. 639210
639210 is divisible by 2, 3, 5, 6, 10, 11
639210 is not divisible by 4, 8, 9
g. 429714
924714 is divisible by 2, 3, 6, 9
924714 is not divisible by 4, 5, 8, 10, 11
h. 2856
2856 is divisible by 2, 3, 4, 6, 8
2856 is not divisible by 5, 9, 10, 11
i. 3060
3060 is divisible by 2, 3, 4, 5, 6, 9, 10
3060 is not divisible by 8, 11
j. 406839
406839 is divisible by 3
406839 is not divisible by 2, 4, 5, 6, 8, 9, 10, 11
Problem 2
2. Using divisibility tests, determine which of the following numbers divisible by 4 and 8.
a. 572, b. 726352, c. 5500, d. 6000
e. 12159, f. 14560, g. 2108
h. 31795072, i. 1700, j. 215
Solutions:
a. 572
572 is divisible by 4 as its last two digits are divisible by 4. (72 ÷ 4 = 18).
572 is not divisible by 8 as its last three digits are not divisible by 8.
b. 726352
72635 is divisible by 4 as its last two digits are divisible by 4. (52 ÷ 4 = 13).
726352 is divisible by 8 as its last three digits are divisible by 8. (325 ÷ 8 = 44).
c. 5500
5500 is divisible by 4 as its last two digits are zero.
5500 is not divisible by 8 as its last three digits are not divisible by 8.
d. 6000
6000 is divisible by 4 as its last two digits are zero.
60 is divisible by 8 as its last three digits are zero.
e. 12159
12159 is not divisible by 4 as its last two digits are not divisible by 4.
12159 is not divisible by 8 as its last three digits are not divisible by 8.
f. 14560
14560 is divisible by 4 as its last two digits are divisible by 4. (60 ÷ 4 = 15).
14560 is divisible by 8 as its last three digits are divisible by 8. (560 ÷ 8 = 70).
g. 21084
21084 is divisible by 4 as its last two digits are divisible by 4. (84 ÷ 4 = 21).
21084 is not divisible by 8 as its last three digits are not divisible by 8. (084÷ 4=21).
h. 31795072
31795072 is divisible by 4 as its last two digits are divisible by 4. (72 ÷ 4 = 18).
31795072 is divisible by 8 as its last three digits are divisible by 8. (o72 ÷ 4 = 18).
i. 1700
1700 is divisible by 4 as its last two digits are zero.
1700 is not divisible by 8 as its last three digits are not divisible by 8.
j. 2150
2150 is not divisible by 4 as its last two digits are not divisible by 4.
2150 is not divisible by 8 as its last three digits are not divisible by 8.
Problem 3
3. Using divisibility tests, determine which of the following numbers are divisible by 6:
a. .297144, b. 1258, c. 4335, d. 61233
e. 901352, f. 438750, g. 1790184
h. 12583, i. 639210, j. 17852
Solutions:
a. 297144
297144 is divisible by 2 as its ones place is an even number.
297144 is divisible by 3 as sum of its digits is divisible by 3. (2 + 9 + 7 + 1 + 4 + 4 = 27)
Since the number is divisible by both 2 and 3, therefore, it is also divisible by 6.
b. 1258
1258 is divisible by 2 as its ones place is an even number.
1258 is not divisible by 3 as sum of its digits is not divisible by 3. (1 + 2 + 5 + 8= 16)
Since the number is divisible by 2 but not divisible by 3, therefore it is not divisible by 6.
c. 4335
4335 is not divisible by 2 as its ones place is not an even number.
4335 is divisible by 3 as sum of its digits is divisible by 3. (4 + 3 + 3 + 5= 15)
Since the number is not divisible by 2 but divisible by 3, therefore, the number is not divisible by 6.
d. 61233
61233 is not divisible by 2 as its ones place is not an even number.
61233 is divisible by 3 as sum of its digits is divisible by 3. (6 + 1 + 2 + 3 + 3 = 15)
Since the number is not divisible by 2 but divisible by 3, therefore, the number is not divisible by 6.
e. 901352
901352 is divisible by 2 as its ones place is an even number.
901352 is not divisible by 3 as sum of its digits is not divisible by 3.
Since the number is divisible by 2 but not divisible by 3, therefore, the number is not divisible by 6.
f. 438750
438750 is divisible by 2 as its ones place is zero.
438750 is divisible by 3 as sum of its digits is divisible by 3. (4 + 3 + 8 + 7 + 5 + 0 =27)
Since the number is divisible by 2 and 3, therefore, the number is divisible by 6.
g. 1790184
1790184 is divisible by 2 as its ones place is an even number.
1790184 is divisible by 3 as sum of its digits is divisible by 3. (1 + 7 + 9 + 0 + 1 + 8 + 4 = 30)
Since the number is divisible by 2 and 3, therefore, the number is divisible by 6.
h. 12583
12583 is not divisible by 2 as its ones place is not an even number.
12583 is not divisible by 3 as sum of its digits is not divisible by 3. (1 + 2 + 5 + 8 + 3 = 19)
Since the number is divisible by 2 but not divisible by 3, therefore, the number is not divisible by 6.
i. 639210
639210 is divisible by 2 as its ones place is zero.
639210 is divisible by 3 as sum of its digits is divisible by 3. (6 + 3 + 9 + 2 + 1 + 0 = 21)
Since the number is divisible by 2 and 3, therefore, the number is divisible by 6.
j. 17892
17892 is divisible by 2 as its ones place is an even number.
17892 is not divisible by 3 as sum of its digits is not divisible by 3.
Since the number is divisible by 2 but not divisible by 3, therefore, the number is not divisible by 6.
Problem 4
4. Using divisibility tests, determine which of the following numbers are divisible by 11:
a. 5445 b. 10824, c. 7138965
d. 70169308 e. 10000001, f. 90115
Solutions:
a. 5445
The sum of the digits at odd places = 5 + 4 = 9
The sum of the digits at even places = 4 + 5 = 9
The difference of both the sums = 9 – 9 = 0
Since the difference is o, therefore, the number is divisible by 11.
b. 10824
The sum of the digits at odd places = 4 + 8 + 1 = 13
The sum of the digits at even places = 2 + 0 = 2
The difference of both the sums = 13 – 2 = 11
Since the difference is 11, therefore, the number is divisible by 11.
c. 7138965
The sum of the digits at odd places = 5 + 9 + 3 + 7 = 24
The sum of the digits at even places = 6 + 8 + 1 = 15
The difference of both the sums = 24 – 15 = 9
Since the difference is o nor 11, therefore, the number is not divisible by 11.
d. 70169308
The sum of the digits at odd places = 8 + 3 + 6 + 0 = 17
The sum of the digits at even places = 0 + 9 + 1 + 7 = 17
The difference of both the sums = 17 – 17 = 0
Since the difference is o, the number is divisible by 11.
e. 10000001
The sum of the digits at odd places = 1 + 0 + 0 + 0 = 1
The sum of the digits at even places = 0 + 0 + 0 + 1 = 1
The difference of both the sums = 1- 1 = 0
Since the difference is o, the number is divisible by 11.
Problem 5
5. Write the smallest digit and the greatest digit in the blank space of each of the following number formed is divisible by 3:
a. _ 6724, b. 4765 _ 2
Solution:
a. _6724
If the blank is x, for the smallest digit number.
The sum of the digits = x + 6 + 7 + 2 + 4 = x + 19
If x= 0, the sum of the digits = 0 + 6 + 7 + 2 + 4 = 19 is not divisible by 3
If x= 1, the sum of the digits = 1 + 6 + 7 + 2 + 4 = 20 is not divisible by 3
If x= 2, the sum of the digits = 2 + 6 + 7 + 2 + 4 = 21 is divisible by 3
Therefore, the smallest digit is 2 in the blank space.
The number is 26724 and is divisible by 3.
For the greatest digit number
If x= 9, the sum of the digits = 9 + 6 + 7 + 2 + 4 = 28 is not divisible by 3
If x= 8, the sum of the digits = 8 + 6 + 7 + 2 + 4 = 27 is divisible by 3
Therefore, the greatest digit is 8 in the blank space.
The number is 86724.It is divisible by 3.
a. 4765_2
If blank is x. For smallest digit number.
The sum of the digits = 4 + 7 + 6 + 5 + x + 2 = x + 24
If x= 0, the sum of the digits = 4 + 7 + 6 + 5 + 0 + 2 = 24. It is divisible by 3.
Therefore, the smallest digit is 0 in the blank space.
The number is 476502. It is divisible by 3.
For the greatest digit number
If x= 9, the sum of the digits = 4 + 7 + 6 + 5 + 9 + 2= 33. It is divisible by 3.
Therefore, the greatest digit is 9 in the blank space.
The number is 476592. It is divisible by 3.
Problem 6
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, b. 8_9484
Solutions:
a. 92_389
The sum of the digits at odd places = 9 + 3 + 2 = 14
The sum of the digits at even places = 8 + x + 9 = x + 17
The difference of the two sums = (x + 17) – 14 = x + 17 – 14 = x + 3
The difference is either o or divisible by 11, then the number is divisible by 11.
Therefore x + 3 =11
x = 11 – 3 = 8
The digit in the blank is 8.
Since the number is 928389.
b. 8_9484
The sum of the digits at odd places = 4 + 4 + x = x + 8
The sum of the digits at even places = 8 + 9 + 8 = 25
The difference of the two sums = 25 – (x + 8) = – x – 8 + 25 = – × + 17
The difference is either o or divisible by 11, then the number is divisible by 11.
Therefore – x + 17 = 11
– x = – 17 + 11= – 6
Therefore, x = 6
The digit in the blank is 6.
Since the number is 869484
Note: Observe the solutions and try them in your own method.
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