NCERT Class 6 Mathematics Chapter 3 Solutions | Playing With Numbers

You will find practice problems and solutions for Class 6 NCERT Mathematics Chapter 3 – Playing With Numbers. The first part of this lesson can be found here. Chapter wise solutions of class 6 mathematics can be found here.

Chapter 3 | Playing With Numbers

Exercise 3.3

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) 31795072
i) 1700
j) 2150

Ans.

A number with 3 or more digits is divisible by 4 if the number formed by its last two digits is divisible by 4.
A number with 4 or more digits is divisible by 8, if the number formed by the last three digits is divisible by 8

a) 572

The last two digit is 72 which is divisible by 4.So 572 is divisible by 4.
The last three digit is 572 which is not divisible by 8.So 572 is not divisible by 8.

b) 726352

The last two digit is 52 which is divisible by 4.So 726352 is divisible by 4.
The last three digit is 352 which is divisible by 8.So 726352 is divisible by 8.

c) 5500

Since the last two digits are 00, the given number is divisible by 4.
The last three digits is 500, which is not divisible by 8.So 5500 is not divisible by 8.

d). 6000

Since the last two digits are 00 and the last three digits are 000, the given number is both divisible by 4 and 8.

e) 12159

The last two digits are 59, which is not divisible by 4.So 12159 is not divisible by 4.
The last three digits are 159, which is not divisible by 8. So 12159 is not divisible by 8.

f) 14560

The last two digits are 60, which is divisible by 4.So 14560 is divisible by 4.
The last three digits are 560, which is divisible by 8.So 14560 is divisible by 8.

g) 21084

The last two digits are 84, which is divisible by 4.So 21084 is divisible by 4.
The last three digits are 084, which is not divisible by 8.So 21084 is not divisible by 8.

h) 31795072

The last two digits are 72, which is divisible by 4.So 31795072 is divisible by 4.
The last three digits are 072, which is divisible by 8.So 31705072 is divisible by 8.

i) 1700

The last two digits are 00, which is divisible by 4.So 1700 is divisible by 4.
The last three digits are 700, which is not divisible by 8.So 1700 is not divisible by 8.

j) 2150

The last two digits are 50, which is not divisible by 4.So 2150 is not divisible by 4.
The last three digits are 150, which is not divisible by 8.So 2150 is not divisible by 8.

3. Using divisibility tests, determine which of 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

Ans. If a number is divisible by 2 and 3 both then it is divisible by 6 also.

a) 297144

Since it is an even number, 297144 is divisible by 2.
Sum of the digits = 2 + 9 + 7 +1 +4 + 4 = 27, which is a multiple of 3.So 297144 is divisible by 3.
Since the given number is divisible by both 2 and 3, 297144 is divisible by 6.

b) 1258

Since the given number is even number, 1258 is divisible by 2.
Sum of the digits = 1 +2 +5 + 8 = 16, which is not a multiple of 3.So 1258 is not divisible by 3.
So 1258 is not divisible by 6.

c) 4335

Since the given number is an odd number, it is not divisible by 2.
Sum of the digits = 4 + 3 + 3 + 5 = 15, which is a multiple of 3.
So 4335 is not divisible by 6.

d) 61233

Since the given number is an odd number, 61233 is not divisible by 2.
Sum of the digits = 6 + 1+ 2+ 3+ 3 = 15, which is a multiple of 3.So 61233 is divisible by 3.
So 61233 is not divisible by 6

e) 901352

Since the given number is an even number, 901352 is divisible by 2.
Sum of the digits = 9 + 0 + 1 +3 + 5 + 2 = 20, which is not a multiple of 3.So 901352 is not divisible by 3.
So 901352 is not divisible by 6.

f) 438750

Since the given number is an even number, 438750 is divisible by 2.
Sum of the digits = 4 + 3 + 8 + 7 + 5 + 0 = 27, which is a multiple of 3.
So it is divisible by 3

So 438750 is divisible by 6.

g) 1790184

Since the given number is an even number, it is divisible by 2.
Sum of the digits = 1 +7 +9+ 0+ 1+ 8+ 4 = 30, which is a multiple of 3.So 1790184 is divisible by 3
Since the given number is divisible by both 2 and 3, it is divisible by 6 also.

h)12583

Since the given number is an odd number, 12583 is not divisible by 2.
Sum of the digits = 1 + 2 + 5 + 8 + 3 = 19, which is not a multiple of 3 .So it is not divisible by 3.
So 12583 is not divisible by 6.

i) 639210

Since the given number is an even number, it is divisible by 2.
Sum of the digits = 6+ 3+ 9+ 2+ 1+ 0 = 21, which is a multiple of 3.So it is divisible by 3.
So 639210 is divisible by 6, since it is divisible by both 2 and 3.

j) 17852

Since the given number is an even number, it is divisible by 2.
Sum of the digits = 1+ 7+ 8+5+2 = 23, which is not a multiple of 3.So it is not divisible by 3.
So 17852 is not divisible by 6.

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
b) 4765–2

Ans.

a) A number is divisible by 3 if the sum of all digits is a multiple of 3.

Consider the smallest digit as 2.Then 26724 is the required number. Sum of the digits

= 2 +6+ 7+ 2+ 4 = 21, which is a multiple of 3.So divisible by 3

Consider the greatest digit as 8 .Then 86724 is the required number. Sum of the digits

= 8 +6+ 7+ 2+ 4 = 27, which is a multiple of 3.So divisible by 3.

b) Consider the smallest number as 0.Then 476502 is the required number.

Sum of the digits = 4 +7+ 6+5+0+2 =24, which is a multiple of 3.So is divisible by 3.
Consider the greatest number as 9. Then 476592 is the required number.
Sum of the digits = 4 +7+6+5+9+2 = 33, which is a multiple of 3.So is divisible by3.

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
Ans.

A number is divisible by 11 if the difference of the sum of the digits at odd places and that of even places should be either 0 or 11.

a) 928389

Sum at odd places = 9 +3+2= 14
Sum at even places = 8 +8+9 = 25
Difference = 25 – 14 = 11

b) 869484

Sum at odd places = 4 +4+ 6 = 14
Sum at even places = 8 +9+ 8 = 25
Difference = 25 – 14 = 11

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