Playing With Numbers
Exercise 2.3 (Prime and Composite Numbers)
Question 1 (Refer Book  Mathematics Class VI R.D. Sharma) 
Solution: 
A number is called a prime number if it has no factor other than 1 and the number itself. Prime numbers between 1 and 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. 
Question 2 (Refer Book  Mathematics Class VI R.D. Sharma) 
Solution: 
i. 10 and 50 Prime numbers between 10 and 50 are 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47.
ii. 70 and 90 Prime numbers between 70 and 90 are 71, 73, 79, 83 and 89.
iii. 40 and 85 Prime numbers between 40 and 85 are 41, 43, 47, 53, 59, 61, 67, 71, 73, 79 and 83.
iv. 60 and 100 Prime numbers between 60 and 100 are 61, 67, 71, 73, 79, 83, 89 and 97. 
Question 3 (Refer Book  Mathematics Class VI R.D. Sharma) 
Solution: 
The smallest prime number is 2. Yes, it is an even number.

Question 4 (Refer Book  Mathematics Class VI R.D. Sharma) 
Solution: 
The smallest odd prime is 3. No, every odd number is not a prime number. Example 9 is an odd number but not a prime.

Question 5 (Refer Book  Mathematics Class VI R.D. Sharma) 
Solution: 
A number is called a composite number if it has at least one factor other than 1 and the number itself. Yes, a composite number can be an odd number. The smallest odd composite number is 9. 
Question 6 (Refer Book  Mathematics Class VI R.D. Sharma) 
Solution: 
Two prime numbers are known as twinprimes if there is only one composite number between them. Twinprimes between 50 and 100 are 59, 61; 71,73

Question 7 (Refer Book  Mathematics Class VI R.D. Sharma) 
Solution: 
Two numbers are said to be coprime if they do not have a common factor other than 1. Example: 2, 3; 3, 4; 5, 6; 8, 13; 12, 23. No, coprimes are not always primes. Example: 15 and 16 are coprime but none of them is prime.

Question 8 (Refer Book  Mathematics Class VI R.D. Sharma) 
Solution: 
i. two prime numbers 
Question 9 (Refer Book  Mathematics Class VI R.D. Sharma) 
Solution: 
i. 13 = 3+3+7 ii. 130 = 59+71 iii. 180 = 79+101

Question 10 (Refer Book  Mathematics Class VI R.D. Sharma) 
Solution: 
i. 36 = 7+29 ii. 42 = 5+37 iii. 84 = 17+67

Question 11 (Refer Book  Mathematics Class VI R.D. Sharma) 
Solution: 
i. 31 = 5+7+19 ii. 35 = 5+7+23 iii. 49 = 3+5+41

Question 12 (Refer Book  Mathematics Class VI R.D. Sharma) 
Solution: 
i. 36 = 17+19 ii. 84 = 41+43 iii. 120 = 59+61

Question 13 (Refer Book  Mathematics Class VI R.D. Sharma) 
Solution: 
i. 29, 31 ii. no twin iii. 101, 103

Question 14 (Refer Book  Mathematics Class VI R.D. Sharma) 
Solution: 
i. All are coprimes ii. Primes  59, 61; 71, 73 iii. Composites – 55, 57; 63, 65

Question 15 (Refer Book  Mathematics Class VI R.D. Sharma) 
Solution: 
1, 3, 7, 9

Question 16 (Refer Book  Mathematics Class VI R.D. Sharma) 
Solution: 
Seven consecutive composite numbers less than 100 so that there is no prime number between them are 90, 91, 92, 93, 94 and 95.

Question 17 (Refer Book  Mathematics Class VI R.D. Sharma) 
Solution: 
i. False ii. True iii. False iv. False v. False vi. False vii. True

Question 18 (Refer Book  Mathematics Class VI R.D. Sharma) 
Solution: 
i. Prime Number ii. Composite Number iii. Prime, Composite iv. 2 v. 4
