Gujarat Board GSEB Textbook Solutions Class 6 Maths Chapter 3 Playing With Numbers Ex 3.2 Textbook Questions and Answers.
Gujarat Board Textbook Solutions Class 6 Maths Chapter 3 Playing With Numbers Ex 3.2
Question 1.
What is the sum of any two.
(a) odd numbers?
(b) even numbers?
Solution:
(a) The sum of any two odd numbers is even.
(b) The sum of any two even numbers is even.
Question 2.
Stare whether the following statements are True or False:
(a) The sum of three odd numbers is even.
(b) The sum of two odd numbers and one even number is even.
(c) The product of three odd numbers is odd.
(d) If an even number is divided by 2 the quotient is always odd.
(e) All prime numbers are odd.
(f) Prime numbers do not have any factors.
(g) Sum of two prime numbers is always even.
(h) 2 is the only even prime number
(i) All even numbers are composite numbers.
(j) The product of two even numbers is always even.
Solution:
(a) False
(b) True
(c) True
(d) False
(e) False
(f) False
(g) False ( 2 + 3 = 5)
(h) True
(i) False ( 2 is an even and prime)
(j) True
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.
Solution:
We know that prime numbers up to 100 are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79 and 97
Obviously, out of these (except 13 and 31) the required pair of prime numbers having same digits are:
(17 and 71); (37 and 73) and (79 and 97).
Question 4.
Write down separately the prime and composite numbers less than 20.
Solution:
Numbers below 20 are:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18 and 19
Since, 1 is neither a prime nor a composite,
out of these numbers,
the prime numbers are: 2, 3, 5, 7, 11, 13, 17 and 19.
Remaining all other numbers are composite numbers.
Composite numbers below 20 are: 4, 6, 8, 9, 10, 12, 14, 15, 16 and 18.
Question 5.
What is the greatest prime number between 1 and 10?
Solution:
Since prime numbers between 1 and 10 are 2, 3, 5 and 7
The greatest prime number between 1 and 10 is 7.
Question 6.
Express the following as the sum of two odd primes.
(a) 44
(b) 36
(c) 24
(d) 18
Solution:
(a) 44 = 13 + 31 or 44 = 3 + 41 or 44 = 7 + 37
(b) 36 = 5 + 31 or 36 = 23 + 13 or 36 = 17 + 19
(c) 24 = 11 + 13 or 24 = 5 + 19 or 247 + 17
(d) 18 = 7 + 11 or 18 = 5 + 13
Question 7.
Give three pairs of prime numbers whose difference is 2.
Solution:
Note: Two prime numbers whose difference is 2 are called twin primes.
Three pairs of prime numbers whose difference is 2 are:
(i) 3 and 5
(ii) 5 and 7
(iii) 11 and 13
Question 8.
Which of the following numbers are prime?
(a) 23
(b) 51
(c) 37
(d) 26
Solution:
(a) 23 = 23 x 1
Factors of 23 are 1 and 23 itself.
Thus, 23 is a prime number.
(b) 51 = 1 x 51 = 3 x 17
Factors of 51 are 1, 3, 17 and 51.
Thus, 51 is not a prime number.
(c) 37 = 1 x 37
Factors of 37 are 1 and 37.
37 is a prime number.
(d) 26 = 1 x 26 = 2 x 13
Factors of 26 are 1, 2, 13 and 26.
26 is not a prime number.
Question 9.
Write seven consecutive composite numbers less than 100 so that there is no prime number between them.
Solution:
The required seven consecutive composite numbers less than 100 are:
90, 91, 92, 93, 94, 95, 96.
Question 10.
Express each of the following numbers as the sum of three odd primes:
(a) 21
(b) 31
(c) 53
(d) 61
Solution:
(a) 21
Wehave, 21 = 3 + 5 + 13
(b) 31
We have, 31 = 3 + 5 + 23
(c) 53
We have, 53 = 13 + 17+ 23
(d) 61
Wehave, 61 = 7 + 13 +41
Question 11.
Write five pairs of prime numbers less than 20 whose sum is divisible by 5.
Hint: 3 + 7 = 10
Solution:
Prime numbers less 20 are: 2, 3, 5, 7, 11, 13, 17 and 19.
We have:
2 + 3 = 5 and 5 is divisible by 5.
3 + 7 = 10 and 10 is divisible by 5.
2 + 13 = 15 and 15 is divisible by 5.
7 + 13 = 20 and 20 is divisible by 5.
3 + 17 = 20 and 20 is divisible by 5.
required prime numbers are:
(i) 2 and 3
(ii) 3 and 7
(iii) 2 and 13
(iv) 7 and 13
(v) 3 and 17
Question 12.
Fill in the blanks.
(a) A number which has only two factors is called a …………….
(b) A number which has more than two factors is called a …………….
(c) 1 is neither ……………. nor …………….
(d) The smallest prime number is …………….
(e) The smallest composite number is …………….
(f) The smallest even number is ……………..
Solution:
(a) prime number
(b) composite number
(c) prime, composite
(d) 2
(e) 4
(f) 2