• Support PF! Buy your school textbooks, materials and every day products Here!

Discrete math question?

  • Thread starter cragar
  • Start date
  • #1
2,544
2

Homework Statement


How many positive divisors does each of the following have?

[tex] 2^n [/tex] where n is a positive integer.
and 30

The Attempt at a Solution


for 30 i get 2 , 5 , 3 , 10
but my book says 2 ,3 ,5 I dont understand why 10 isn't a divisor.
and for 2^n im trying to look for a pattern if n=1 i get no divisors
and n=2 i get 1 divisor and n=3 i get 2 divisors so would it be
2^n has n-1 divisors?
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,832
251
hi cragar! :smile:

(try using the X2 tag just above the Reply box, and write "itex" rather than "tex", and it won't keep starting a new line :wink:)
How many positive divisors does each of the following have?

for 30 i get 2 , 5 , 3 , 10
but my book says 2 ,3 ,5
i suspect that that's just a hint, and they're telling you those are the prime divisors, and leaving you to carry on from there

(btw, you've missed out two more)
and for 2^n im trying to look for a pattern if n=1 i get no divisors
and n=2 i get 1 divisor and n=3 i get 2 divisors so would it be
2^n has n-1 divisors?
yes :smile:

(though you should be able to prove it more rigorously than that! :wink:)
 
  • #3
2,544
2
ok thanks for your post. so would all the divisors of 30 be 1 , 2 ,5,6,10 ,15 . is one a divisor. for [itex] 2^n [/itex] to have divisors it has to be a multiple of 2 so would I divide it by 2 and then i would get [itex] 2^{n-1} [/itex]
then could i say it has n-1 divisors
 
  • #4
tiny-tim
Science Advisor
Homework Helper
25,832
251
hi cragar! :wink:
would all the divisors of 30 be 1 , 2 ,5,6,10 ,15 .
yes :smile: (except i don't know whether 1 counts as a divisor :redface:)
for [itex] 2^n [/itex] to have divisors it has to be a multiple of 2 so would I divide it by 2 and then i would get [itex] 2^{n-1} [/itex]
then could i say it has n-1 divisors
better would be …

2n has only one prime divisor, 2 …

so its only divisors are 2k for 0 < k < n, of which there are n - 1 :wink:

(and now try a similar proof for 30 :biggrin:)
 

Related Threads on Discrete math question?

  • Last Post
Replies
1
Views
879
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
0
Views
811
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
15
Views
2K
  • Last Post
Replies
5
Views
1K
Top