+0  
 
0
61
1
avatar

How many natural numbers less than 1000 have exactly three distinct positive integer divisors?

Guest Jun 25, 2018
 #1
avatar+88962 
+2

This seems tougher than it really  is

 

Note....that every  non-square natural number will have an even number of divisors

 

For instance.....the divisors  of 8  are  1  2  4  8

 

However....the perfect squares always  have an odd number of divisors

 

For instance....the divsors of 16  are  1  2  4  8  and 16

 

And  the perfect squares  which have prime square roots  will  only  have 3 divisors

 

For instance...9   has a square root of 3 which is prime....so...it will only have 3 divisors  ⇒ 1, 3 and 9

 

So...the squares  < 1000  which have prime square roots are

 

4            289

9            361

25          529

49          841

121        961

169

 

So...11  natural numbers < 1000   have  only 3 divisors

 

 

cool cool cool

CPhill  Jun 25, 2018

30 Online Users

avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.