1. Example-1
1. greatest prime number between 1 and 10
Solution:
Number | Factors | Prime or Composite? | 1 | 1 | neither Prime nor Composite | 2 | 1,2 | Prime | 3 | 1,3 | Prime | 4 | 1,2,4 | Composite | 5 | 1,5 | Prime | 6 | 1,2,3,6 | Composite | 7 | 1,7 | Prime | 8 | 1,2,4,8 | Composite | 9 | 1,3,9 | Composite | 10 | 1,2,5,10 | Composite |
Prime numbers : between 1 and 10 2, 3, 5, 7
There are 4 prime numbers between 1 and 10
Maximum is 7
2. greatest prime number between 1 and 20
Solution:
Number | Factors | Prime or Composite? | 1 | 1 | neither Prime nor Composite | 2 | 1,2 | Prime | 3 | 1,3 | Prime | 4 | 1,2,4 | Composite | 5 | 1,5 | Prime | 6 | 1,2,3,6 | Composite | 7 | 1,7 | Prime | 8 | 1,2,4,8 | Composite | 9 | 1,3,9 | Composite | 10 | 1,2,5,10 | Composite | 11 | 1,11 | Prime | 12 | 1,2,3,4,6,12 | Composite | 13 | 1,13 | Prime | 14 | 1,2,7,14 | Composite | 15 | 1,3,5,15 | Composite | 16 | 1,2,4,8,16 | Composite | 17 | 1,17 | Prime | 18 | 1,2,3,6,9,18 | Composite | 19 | 1,19 | Prime | 20 | 1,2,4,5,10,20 | Composite |
Prime numbers : between 1 and 20 2, 3, 5, 7, 11, 13, 17, 19
There are 8 prime numbers between 1 and 20
Maximum is 19
3. greatest prime number between 1 and 50
Solution:
Number | Factors | Prime or Composite? | 1 | 1 | neither Prime nor Composite | 2 | 1,2 | Prime | 3 | 1,3 | Prime | 4 | 1,2,4 | Composite | 5 | 1,5 | Prime | 6 | 1,2,3,6 | Composite | 7 | 1,7 | Prime | 8 | 1,2,4,8 | Composite | 9 | 1,3,9 | Composite | 10 | 1,2,5,10 | Composite | 11 | 1,11 | Prime | 12 | 1,2,3,4,6,12 | Composite | 13 | 1,13 | Prime | 14 | 1,2,7,14 | Composite | 15 | 1,3,5,15 | Composite | 16 | 1,2,4,8,16 | Composite | 17 | 1,17 | Prime | 18 | 1,2,3,6,9,18 | Composite | 19 | 1,19 | Prime | 20 | 1,2,4,5,10,20 | Composite | 21 | 1,3,7,21 | Composite | 22 | 1,2,11,22 | Composite | 23 | 1,23 | Prime | 24 | 1,2,3,4,6,8,12,24 | Composite | 25 | 1,5,25 | Composite | 26 | 1,2,13,26 | Composite | 27 | 1,3,9,27 | Composite | 28 | 1,2,4,7,14,28 | Composite | 29 | 1,29 | Prime | 30 | 1,2,3,5,6,10,15,30 | Composite | 31 | 1,31 | Prime | 32 | 1,2,4,8,16,32 | Composite | 33 | 1,3,11,33 | Composite | 34 | 1,2,17,34 | Composite | 35 | 1,5,7,35 | Composite | 36 | 1,2,3,4,6,9,12,18,36 | Composite | 37 | 1,37 | Prime | 38 | 1,2,19,38 | Composite | 39 | 1,3,13,39 | Composite | 40 | 1,2,4,5,8,10,20,40 | Composite | 41 | 1,41 | Prime | 42 | 1,2,3,6,7,14,21,42 | Composite | 43 | 1,43 | Prime | 44 | 1,2,4,11,22,44 | Composite | 45 | 1,3,5,9,15,45 | Composite | 46 | 1,2,23,46 | Composite | 47 | 1,47 | Prime | 48 | 1,2,3,4,6,8,12,16,24,48 | Composite | 49 | 1,7,49 | Composite | 50 | 1,2,5,10,25,50 | Composite |
Prime numbers : between 1 and 50 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
There are 15 prime numbers between 1 and 50
Maximum is 47
4. greatest prime number between 1 and 100
Solution: Prime numbers : between 1 and 100 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
There are 25 prime numbers between 1 and 100
Maximum is 97
5. least prime number between 50 and 60
Solution:
Number | Factors | Prime or Composite? | 50 | 1,2,5,10,25,50 | Composite | 51 | 1,3,17,51 | Composite | 52 | 1,2,4,13,26,52 | Composite | 53 | 1,53 | Prime | 54 | 1,2,3,6,9,18,27,54 | Composite | 55 | 1,5,11,55 | Composite | 56 | 1,2,4,7,8,14,28,56 | Composite | 57 | 1,3,19,57 | Composite | 58 | 1,2,29,58 | Composite | 59 | 1,59 | Prime | 60 | 1,2,3,4,5,6,10,12,15,20,30,60 | Composite |
Prime numbers : between 50 and 60 53, 59
There are 2 prime numbers between 50 and 60
Minimum is 53
6. least prime number between 100 and 110
Solution: Prime numbers : between 100 and 110 101, 103, 107, 109
There are 4 prime numbers between 100 and 110
Minimum is 101
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