We say that a positive integer is quiteprime if it is not divisible by 2, 3, or 5. How many quiteprime positive integers are there less than 100? Less than 1000? A positive integer is very quiteprime if it is not divisible by any prime less than 15. How many very quiteprime positive integers are there less than 90000? Without giving an exact answer, can you say approximately how many very quiteprime positive integers are less than 1010? Less than 10100? Explain your reasoning as carefully as you can.
Answers
Answer:
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Answer:
Quite Prime positive integers less than 100 = 25
Step-by-step explanation:
We say that a positive integer is quiteprime if it is not divisible by 2, 3, or 5. How many quiteprime positive integers are there less than 100?
Total number between 2 to 100 = 99
Number divisible by 2 = 2 , 4 , .... 98 , 100 = 50
Number divisible by 3 = 3 , 6 , .....96 , 99 = 33
Number Divisible by 5 = 5 , 10, .....95 , 100 = 20
2∩3 - Number divisible by 2 & 3 means by 6 = 6 , 12 ..... 90 , 96 = 16
3∩5 - Number Divisible by 3 & 5 means by 15 = 15 , 30 ,....75 , 90 = 6
2∩5 - Number Divisible by 2 & 5 means by 10 = 10 , 20 ,....90 , 100 = 10
2∩3∩5 Number Divisible by 2 , 3 & 5 measn by 30 = 30 , 60 , 90 = 3
Number Divisible by 2 + Number Divisible by 3 + Number Divisible by 5 = 50 + 33 + 20 - 16 - 6 - 10 + 3 = 74
(as 2∪3∪5 = 2 + 3 + 5 - 2∩3 -3∩5-2∩5+2∩3∩5)
Quite Prime positive integers = 99 - 74 = 25
Quite Prime positive integers less than 100 = 25
Numbers are
7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 77 79 83 89 91 93 97