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How many integers less than 1000 have no factors (other than 1) in com

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GeminiHeat
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How many integers less than 1000 have no factors (other than 1) in com [#permalink] New post   20 Sep 2021, 04:55
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How many integers less than 1000 have no factors (other than 1) in common with 1000?

A. 400

B. 401

C. 410

D. 420

E. 421
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eskay1981
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Re: How many integers less than 1000 have no factors (other than 1) in com [#permalink] New post   21 Sep 2021, 06:20
GeminiHeat wrote:
How many integers less than 1000 have no factors (other than 1) in common with 1000?


Number of integers less than 1000 = 1000 - 1 = 999,
Factors of 1000 are 2^3 * 5^3. So just check for prime factors 2 and 5.
Factors of 2 are 1/2 the numbers from 2 to 998 = 499
and Factors of 5, but not 2 are 5,15,...995 = 100
So 999 - 499 - 100 = 400.

Answer is A) 400
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gmatclubot
Re: How many integers less than 1000 have no factors (other than 1) in com [#permalink]
21 Sep 2021, 06:20
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