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The number of positive integers less than 2009 that have exactly three prime factors, not necessarily distinct, such that each p rime factor is greater than 10 is -------------------

The number of positive integers less than 2009 that have exactly three prime factors, not necessarily distinct, such that each p rime factor is greater than 10 is -------------------

Grade:12th pass

1 Answers

Pramod J AskiitiansExpert-IIT-B
36 Points
13 years ago

The number of positive integers less than 2009 that have exactly three prime factors, not necessarily distinct, such that each p rime factor is greater than 10 is

prime numbers grater than 10 are 11,13,17,... etc

13^3 = 2197 > 2009

11^3 = 1331 < 2009

this implies there is only one number less than 2009 that have exactly three prime factors, not necessarily distinct, such that each p rime factor is greater than 10

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