anonymous
  • anonymous
How many positive integers less than or equal to 2000 have an odd number of factors?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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jim_thompson5910
  • jim_thompson5910
Hint: look at the factorizations of the first 10 positive whole numbers and see which number has an odd number of factors
anonymous
  • anonymous
I'll look and see... wait a second
jim_thompson5910
  • jim_thompson5910
ok

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More answers

anonymous
  • anonymous
From 1-10 would only be the number 1; srry I kinda had to go do something for a sec
jim_thompson5910
  • jim_thompson5910
you're fine
jim_thompson5910
  • jim_thompson5910
you sure only 1 has an odd number of factors?
anonymous
  • anonymous
and 4
jim_thompson5910
  • jim_thompson5910
what else
anonymous
  • anonymous
and 9
jim_thompson5910
  • jim_thompson5910
what do you notice
anonymous
  • anonymous
Can't really think of anything
anonymous
  • anonymous
Can you give me a hint?
jim_thompson5910
  • jim_thompson5910
1, 4, 9, ... hmm
jim_thompson5910
  • jim_thompson5910
what kind of sequence is that
jim_thompson5910
  • jim_thompson5910
if you're not sure, look at the next ten numbers (11 through 20) and take note which numbers have an odd number of factors
anonymous
  • anonymous
Sounds like +3, +5, maybe then +7
anonymous
  • anonymous
Yup this works:)
jim_thompson5910
  • jim_thompson5910
that's one way to look at it, but there's another
jim_thompson5910
  • jim_thompson5910
the extended sequence is 1, 4, 9, 16, 25, 36, 49, ...
jim_thompson5910
  • jim_thompson5910
each number is a perfect _____
anonymous
  • anonymous
Oh I didn't notice that
jim_thompson5910
  • jim_thompson5910
so all you have to do is count the number of perfect squares less than 2000 use this list: http://www.mathwarehouse.com/arithmetic/numbers/list-of-perfect-squares.php or you can take the square root of 2000 to get 44.7213595499958 this means that 44^2 = 1936 is the largest perfect square that is less than 2000 anything higher (like 45^2) is going to be over 2000
anonymous
  • anonymous
On this problem I'm supposably not supposed to use a list, so if 44^2 is the largest perfect square does that mean that I should count all the perfect squares 44^2 and below?
jim_thompson5910
  • jim_thompson5910
yep, so 1^2, 2^2, 3^2, ..., 41^2, 42^2, 43^2, 44^2 all work
anonymous
  • anonymous
Would 1^3 work too though?
jim_thompson5910
  • jim_thompson5910
1^2 = 1 is a perfect square
jim_thompson5910
  • jim_thompson5910
1 only has 1 factor (itself), so it has an odd number of factors
jim_thompson5910
  • jim_thompson5910
1^3 is still 1, but technically not the same
jim_thompson5910
  • jim_thompson5910
because if you cubed 2, you would get 2^3 = 8, but 8 doesn't have an odd number of factors
anonymous
  • anonymous
Oh, so 44 positive integers or is it more complicated than what I'm thinking?
jim_thompson5910
  • jim_thompson5910
yep 44 is your answer and maybe you are, but that's ok, you're thinking about the problem
anonymous
  • anonymous
Thanks:)
jim_thompson5910
  • jim_thompson5910
yw

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