Practice Set 4.1
(1)
Fill in the blanks.
i) .......... number is neither prime nor composite.
ii) .......... is the smallest prime number.
iii) .......... is the only even prime number.
iv) .......... is the smallest odd prime number.
ii) .......... is the smallest prime number.
iii) .......... is the only even prime number.
iv) .......... is the smallest odd prime number.
Solution
i) 1 is neither a prime nor a composite number.
ii) 2 is the smallest prime number.
iii) 2 is the only even prime number.
iv) 3 is the smallest odd prime number.
Ans.
(i) 1
(ii) 2
(iii) 2
(iv) 3
(2)
Write five pairs of coprime numbers between 1 and 50.
Solution
We can write any five pairs of coprime numbers between 1 and 50.
(i)
(4, 9)
(ii)
(7, 10)
(iii)
(11, 12)
(iv)
(13, 14)
(v)
(17, 20)
Ans.
(i) (4, 9)
(ii) (7, 10)
(iii) (11, 12)
(iv) (13, 14)
(v) (17, 20)
(3)
Complete the pattern of prime numbers.
2,
,
5, 7,
,
13, 17,
,
23, 29,
,
37,
,
,
47.
Solution
2,
3
5, 7,
11
13, 17,
19
23, 29,
31
37,
41
43
47.
Ans.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.
(4)
Identify the 'twin prime' numbers from the following and write a reason why they are twin prime numbers.
i) 3 and 5
ii) 7 and 9
iii) 11 and 13
iv) 23 and 29
v) 29 and 31
vi) 41 and 47
ii) 7 and 9
iii) 11 and 13
iv) 23 and 29
v) 29 and 31
vi) 41 and 47
Solution
(i) 3 and 5
Ans.
3 and 5 are twin prime numbers because they are prime numbers
with a difference of 2.
(ii) 7 and 9
Ans.
7 and 9 are not twin prime numbers because 9 is not a prime number.
(iii) 11 and 13
Ans.
11 and 13 are twin prime numbers because they are prime numbers
with a difference of 2.
(iv) 23 and 29
Ans.
23 and 29 are not twin prime numbers because the difference
between these prime numbers is not two.
(v) 29 and 31
Ans.
29 and 31 are twin prime numbers because they are prime numbers
with a difference of 2.
(vi) 41 and 47
Ans.
41 and 47 are not twin prime numbers because the difference
between these prime numbers is not two.