NCERT Class 6 Maths Solutions | Lesson 3 | Playing With Numbers

In this chapter we will learn about lesson 3 of class 6 NCERT Maths. Extra practice problems for this chapter can be found here.

You can find solutions of exercise 3.3 of Playing with numbers here.

CLASS 6  | LESSON 3 | PLAYING WITH NUMBERS

EXERCISE 3.1

1. Write all the factors of the following numbers:

a) 24
Ans. We note that
24 = 1 x 24
24 = 2 x 12
24 = 3 x 8
24 = 4 x 6
Thus all the factors of 24 are 1,2,3,4,6,8,12,24

b) 15
Ans. We note that
15 = 1 x 15
15 = 3 x 5
Thus all the factors of 15 are 1, 3,5,15

c) 21
Ans. We note that
21 = 1 x 21
21 = 3 x 7
Thus all the factors of 21 are 1, 3,7,21

d) 27
Ans. We note that
27 = 1 x 27
27 = 3 x 9
Thus all the factors of 27 are 1, 3,9,27

e) 12
Ans. We note that
12 = 1 x 12
12 = 2 x 6
12 = 3 x 4
Thus all the factors of 12 are 1,2,3,4,6,12

f) 20
Ans. We note that
20 = 1 x 20
20 = 2 x 10
20 = 4 x 5
Thus all the factors of 20 are 1, 2,4,5,10,20

g) 18
Ans. We note that
18 = 1 x 18
18 = 2 x 9
18 = 3 x 6
Thus all the factors of 18 are 1,2,3,6,9,18

h) 23
Ans. We note that
23 = 1 x 23
Thus the factors of 23 are 1 and 23 only.23 is a prime number.

i) 36
Ans. We note that
36 = 1 x 36
36 = 2 x 18
36 = 3 x 12
36 = 4 x 9
36 = 6 x 6
Thus all the factors of 36 are 1,2,3,4,6,9,12,18 and 36

2. Write first five multiples of:

a) 5
Ans. 5, 10,15,20,25

b) 8
Ans. 8, 16,24,32,40

c) 9
9, 18,27,36,45

3. Match the items in column 1 with the items in column 2.

Column 1 Column 2
i) 35 a) Multiple of 8
ii) 15 b) Multiple of 7
iii) 16 c) Multiple of 70
iv) 20 d) Factor of 30
v) 25 e) Factor of 50
f) Factor of 20

Ans.

i) 35 —— Multiple of 7
ii) 15 ——Factor of 30
iii) 16 —-Multiple of 8
iv) 20 —-Factor of 20
v) 25 —–Factor of 50

EXERCISE 3.2

1. What is the sum of any two
a) Odd numbers
b) Even numbers
Ans.

a) Even number

b) Even number

2. State whether the following statements are True or False?
a) The sum of three odd numbers is even
Ans. False
b) The sum of two odd numbers and one even number is even.
Ans. True
c) The product of three odd numbers is odd.
Ans. True
d) If an even number is divided by 2, the quotient is always odd.
Ans. False
e) All prime numbers are odd.
Ans. False
f) Prime numbers do not have any factors.
Ans. False
g) Sum of two prime numbers is always even.
Ans. False
h) 2 is the only even prime number.
Ans. True
i) All even numbers are composite numbers.
False
j) The product of two even numbers is always even.
True

3. The numbers 13 and 31 are prime numbers. Both these numbers have same digits 1 and 3.Find such pairs of prime numbers up to 100.

Ans.
17 and 71
37 and 73
79 and 97

4. Write down separately the prime and composite numbers less than 20.

Ans. Prime numbers: 2, 3, 5,7,11,13,17,19
Composite numbers: 4,6,8,9,10,12,14,15,16,18

5. What is the greatest prime number between 1 and 10?
Ans: Seven

6. Express the following as the sum of two odd primes.

a) 44 b) 36 c) 24 d) 18
Ans.

a) 44 = 3 +41
b) 36 = 5 + 31
c) 24 = 5 + 19
d) 18 = 5 +13

7. Give three pairs of prime numbers whose difference is 2.

(Two prime numbers whose difference is 2 are called twin primes)

Ans.
3, 5
5, 7
11, 13

8. Which of the following numbers are prime?

a) 23 b) 51 c) 37 d) 26
Ans. 23 and 37 are prime numbers
51 and 26 are composite numbers.

9. Write seven consecutive composite numbers less than 100 so that there is no prime number between them.
Ans. 90, 91, 92, 93, 94, 95, 96

10. Express each of the following numbers as the sum of three odd primes.
a) 21 b) 31 c) 53 d) 61

Ans.
a) 3 + 5 +13
b) 3 + 5 + 23
c) 13 + 17 + 23
d) 7 + 13 + 41

11. Write five pairs of prime numbers less than 20 whose sum is divisible by 5.
Ans. 2, 3: 2, 13: 3, 17: 7, 13: 11, 19

12. Fill in the blanks:

a) A number which has only two factors is called a …………
Ans. Prime number

b) A number which has more than two factors is called a ……..
Ans. Composite number

c) 1 is neither ………. Nor …………
Ans. Prime number, Composite number

d) The smallest prime number is ………..
Ans. 2

e) The smallest composite number is ………..
Ans. 4

f) The smallest even number is ——–
Ans. 2

EXERCISE 3.3

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)

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