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How many positive integers less than or equal to 100 have a prime factor that is greater than 4?

 Mar 4, 2018
 #1
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5, 7

10, 11, 13, 14, 15, 17, 19

20, 21, 22, 23, 25, 26, 28, 29

30, 31, 33, 34, 35, 37, 38, 39

40, 41, 42, 43, 44, 45, 46, 47, 49

50, 51, 52, 53, 55, 56, 57, 58, 59

60, 61, 62, 63, 65, 66, 67, 68, 69

70, 71, 73, 74, 75, 76, 77, 78, 78

80, 82, 83, 84, 85, 86, 87, 88, 89

90, 91, 92, 93, 94, 95, 97, 98, 99, 100

 

I'll let you count them

 

cool cool cool

 Mar 4, 2018
 #2
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100 - 4 = 96

Since 6 = 2 x 3 and 96/6 = 16, therefore:

96 - 16 = 80 numbers that should have prime factors of 5 and greater.

 Mar 4, 2018

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