EVENTS CONVENT HIGH SCHOOL
15/01/2021 CLASS-6 SLOT-2
MATHS
Chapter-3 PLAYING WITH NUMBERS
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Question 1:Write
all the factors of the following numbers:
(a) 24 (b) 15 (c) 21
(d) 27 (e) 12 (f) 20
(g) 18 (h) 23 (i) 36
Answer:(a)
24
24 = 1 × 24 24 = 2 × 12 24 = 3 × 8
24 = 4 × 6 24 = 6 × 4
∴Factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24
(b) 15
15 = 1 × 15 15 = 3 × 5 15 = 5 × 3
∴Factors of 15 are 1, 3, 5, and 15
(c) 21
21 = 1 × 21 21 = 3 × 7 21 = 7 × 3
∴Factors of 21 are 1, 3, 7, and 21
(d) 27
27 = 1 × 27 27 = 3 × 9 27 = 9 × 3
∴Factors of 27 are 1, 3, 9, and 27
(e) 12
12 = 1 × 12 12 = 2 × 6 12 = 3 × 4 12 = 4 × 3
∴Factors of 12 are 1, 2, 3, 4, 6, and 12
(f) 20
20 = 1 × 20 20 = 2 × 10 20 = 4 × 5 20 = 5 × 4
∴Factors of 20 are 1, 2, 4, 5, 10, and 20
(g) 18
18 = 1 × 18 18 = 2 × 9 18 = 3 × 6 18 = 6 × 3
∴Factors of 18 are 1, 2, 3, 6, 9, and 18
(h) 23
23 = 1 × 23 23 = 23 × 1
∴ Factors of 23 are 1 and 23
(i) 36
36 = 1 × 36 36 = 2 × 18 36 = 3 × 12 36 = 4 × 9
36 = 6 × 6
∴Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36
Question 2:Write
first five multiplies of:(a) 5 (b) 8 (c) 9
Answer:
(a) 5 × 1
= 5 5 × 2 = 10 5 × 3 = 15 5 × 4 = 20 5 × 5 = 25
∴ The
required multiples are 5, 10, 15, 20, and 25.
(b) 8 × 1
= 8 8 × 2 = 16 8 × 3 = 24 8 × 4 = 32 8 × 5 = 40
∴ The
required multiples are 8, 16, 24, 32, and 40.
(c) 9 × 1
= 9 9 × 2 = 18 9 × 3 = 27 9 × 4 = 36 9 × 5 = 45
∴ The required multiples are 9, 18, 27, 36, and 45.
Question 3:Match
the items in column 1 with the items in column 2.
Answer:
|
Column
1 |
Column
2 |
|
(i) 35 |
(b) Multiple of 7 |
|
(ii) 15 |
(d) Factor of 30 |
|
(iii) 16 |
(a) Multiple of 8 |
|
(iv) 20 |
(f) Factor of 20 |
|
(v) 25 |
(e) Factor of 50 |
Page No 51:
Question 4:Find
all the multiples of 9 up to 100.
Answer:
9 × 1 = 9
9 × 2 = 18 9 × 3 = 27 9 × 4 = 36 9 × 5 = 45
9 × 6 = 54
9 × 7 = 63 9 × 8 = 72 9 × 9 = 81 9 × 10 = 90
9 × 11 =
99
Therefore,
the multiples of 9 up to 100 are
9, 18, 27, 36, 45, 54, 63, 72, 81, 90, and 99
Page No 53:
Question 1:What
is the sum of any two (a) Odd numbers? (b) Even numbers?
Answer:
(a) The
sum of two odd numbers is even.
e.g., 1 +
3 = 4
13 + 19 =
32
(b) The
sum of two even numbers is even.
e.g., 2 +
4 = 6
10 + 18 = 28
Question 2: State whether the following statements are True or False:
(a) The sum of three odd numbers is even.
a. False 3 + 5 + 7 = 15, i.e., odd
(b) The sum of two odd numbers and one even number is even.
a. True 3 + 5 + 6 = 14, i.e., even
(c) The product of three odd numbers is odd.
a. True 3 × 5 × 7 = 105, i.e., odd
(d) If an even number is divided by 2, the quotient is always
odd.
a. False 4 ÷ 2 = 2, i.e., even
(e) All prime numbers are odd.
a. False 2 is a prime number and it is also even
(f) Prime numbers do not have any factors.
a. False 1 and the number itself are factors of the number
(g) Sum of two prime numbers is always even.
a. False 2 + 3 = 5, i.e., odd
(h) 2 is the only even prime number.
a. True
(i) All even numbers are composite numbers.
a. False 2 is a prime number
(j) The product of two even numbers is always even.
a. True 2 × 4 = 8, i.e., even
Question 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.
Answer:
17, 71
37, 73
79, 97
Question 4:Write
down separately the prime and composite numbers less than 20.
Answer:
Prime
numbers less than 20 are
2, 3, 5,
7, 11, 13, 17, 19
Composite
numbers less than 20 are
4, 6, 8, 9, 10, 12, 14, 15, 16, 18
Question 5:What
is the greatest prime number between 1 and 10?
Answer:
Prime numbers between 1 and 10 are 2, 3, 5, and 7. Among
these numbers, 7 is the greatest.
Question 6:Express
the following as the sum of two odd primes.
(a) 44 (b) 36 (c) 24 (d) 18
Answer:
(a) 44 =
37 + 7
(b) 36 =
31 + 5
(c) 24 =
19 + 5
(d) 18 = 11 + 7
Question 7:Give
three pairs of prime numbers whose difference is 2.
[Remark: Two prime numbers whose difference is 2 are
called twin primes].
Answer:
3, 5
41, 43
71, 73
Question 8:Which
of the following numbers are prime?
(a) 23 (b) 51 (c) 37 (d) 26
Answer:
(a) 23 23
= 1 × 23 23 = 23 × 1
23 has
only two factors, 1 and 23. Therefore, it is a prime number.
(b) 51 51
= 1 × 51 51 = 3 × 17
51 has
four factors, 1, 3, 17, 51. Therefore, it is not a prime number. It is a
composite number.
(c) 37
It has
only two factors, 1 and 37. Therefore, it is a prime number.
(d) 26
26 has four factors (1, 2, 13, 26). Therefore, it is not
a prime number. It is a composite number.
Question 9:Write
seven consecutive composite numbers less than 100 so that there is no prime
number between them.
Answer:
Between 89
and 97, both of which are prime numbers, there are 7 composite numbers. They
are
90, 91,
92, 93, 94, 95, 96
Numbers
Factors
90 1, 2,
3, 5, 6, 9, 10, 15, 18, 30, 45, 90
91 1, 7,
13, 91
92 1, 2,
4, 23, 46, 92
93 1, 3,
31, 93
94 1, 2,
47, 94
95 1, 5,
19, 95
96 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Page No 54:
Question 10:Express each of the following numbers as the sum of three odd primes:
(a) 21 (b) 31 (c) 53 (d) 61
Answer:
(a) 21 = 3
+ 7 + 11
(b) 31 = 5
+ 7 + 19
(c) 53 = 3
+ 19 + 31
(d) 61 = 11 + 19 + 31
Question 11:Write five pairs of prime numbers less than 20 whose sum is divisible by
5.
(Hint: 3 + 7 = 10)
Answer:
2 + 3 = 5
2 + 13 =
15
3 + 17 =
20
7 + 13 =
20
19 + 11 = 30
Question 12:Fill in the blanks:
(a) A
number which has only two factors is called a Prime number
(b) A
number which has more than two factors is called a Composite number
(c) 1 is
neither Prime number, nor composite number
(d) The
smallest prime number is 2
(e) The
smallest composite number is 4
(f) The smallest even number is 2
