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For positive integer n, function f(n), which is the number of positive

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MathRevolution
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For positive integer n, function f(n), which is the number of positive [#permalink] For positive integer n, function f(n), which is the number of positive   08 Feb 2016, 00:21
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For positive integer n, function f(n), which is the number of positive integers less than n such that have no common factor with n except 1, is n×(1-1/p1 )×(1-1/p2 )×(1-1/p3 )×…. ×(1- 1/pn ), (pi are different prime factors of n). If n=60, what is the value of f(n) ?

A. 12 B. 14 C. 15 D. 16 E. 18

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D
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PrakharGMAT
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For positive integer n, function f(n), which is the number of positive [#permalink] For positive integer n, function f(n), which is the number of positive   05 Mar 2016, 04:43
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60= 2^2 *3*5
No of relatively prime= 60(1-1/2)(1-1/3)(1-1/5) = 16

SO IMO- 16 should be the answer
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Re: For positive integer n, function f(n), which is the number of positive [#permalink] For positive integer n, function f(n), which is the number of positive   28 Jul 2017, 08:03
MathRevolution Can you please post the detailed solution!!!

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Re: For positive integer n, function f(n), which is the number of positive [#permalink] For positive integer n, function f(n), which is the number of positive   18 Sep 2018, 02:39
NandishSS
MathRevolution Can you please post the detailed solution!!!

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Little bit late, but mabybe still helpful for others...

This question basically requires you to find the prime factors of 60! Which are \(2^2\),3,5

When you plug these in in the equation you get --> 60*(1-\(\frac{1}{2}\))*(1-\(\frac{1}{3}\))*(1-\(\frac{1}{5}\))

Which simplifies to --> 60*\(\frac{1}{2}\)*\(\frac{2}{3}\)*\(\frac{4}{5}\) --> 2*2*4=16

Hence D
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Re: For positive integer n, function f(n), which is the number of positive [#permalink] For positive integer n, function f(n), which is the number of positive   26 Sep 2024, 00:39
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Re: For positive integer n, function f(n), which is the number of positive [#permalink]
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