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The function f(n) for an integer n is defined as the number of
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27 May 2018, 10:50
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The function f(n) for an integer n is defined as the number of positive integers that are factors of n. For example, f(6) = 4 because 6 has 4 factors: 1, 2, 3, 6. What is the value of f(f(24^2))? A. 2 B. 4 C. 6 D. 8 E. 12 Source: Experts Global
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The function f(n) for an integer n is defined as the number of
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28 May 2018, 06:47
nigina93 wrote: I would go with B and here is why. First take care of f(24^2) or 576 which has 21 factors (before 24 it has 10 factors(1,2,3,4,6,8,9,12,16,18) + 1 (24) itself +10 factors after 24). Now, we are left with f(21), which has 4 factors (1,3,7,21), asnwer is B. I wonder whether there is easier way of realizing 21 factors of 576, because I do list them manually and took longer than 2 mins, Bunuel? For any number, in order to find the total number of factors of any numbers, we need to do the following steps 1. Prime factorize number to the form \(a^x*b^y*c^z\) where a,b,c are the prime numbers. 2. Total number of prime factors are (x+1)(y+1)(z+1) Let's try and use this to find the number of factors of 576 which is \(24^2\) Primefactorizing \((576)^2\), we get \((24^2)^2 = (2^3*3)^2 = 2^6*3^2\). The number of factors of \((576)^2\) can be given as \((6+1)(2+1) = 7*3 = 21\) Therefore, the value for \(f(f(24^2)) = f(21)\) is 4(Option B)
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The function f(n) for an integer n is defined as the number of
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27 May 2018, 19:56
B
24*24 has 21 factors 21 has 4 factors



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Re: The function f(n) for an integer n is defined as the number of
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28 May 2018, 06:41
I would go with B and here is why. First take care of f(24^2) or 576 which has 21 factors (before 24 it has 10 factors(1,2,3,4,6,8,9,12,16,18) + 1 (24) itself +10 factors after 24). Now, we are left with f(21), which has 4 factors (1,3,7,21), asnwer is B. I wonder whether there is easier way of realizing 21 factors of 576, because I do list them manually and took longer than 2 mins, Bunuel?
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The function f(n) for an integer n is defined as the number of
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28 May 2018, 07:09
nigina93 wrote: I would go with B and here is why. First take care of f(24^2) or 576 which has 21 factors (before 24 it has 10 factors(1,2,3,4,6,8,9,12,16,18) + 1 (24) itself +10 factors after 24). Now, we are left with f(21), which has 4 factors (1,3,7,21), asnwer is B. I wonder whether there is easier way of realizing 21 factors of 576, because I do list them manually and took longer than 2 mins, Bunuel? There IS an easier way. Given \(f(f(24^2))\) For simplicity's sake let \(f(24^2)\)=z ∴ we have f(z). Now lets solve z = \(f(24^2)\) > \(f( (8*3)^2 )\) > \(f((2^3*3)^2)\)  > \(f(2^6*3^2)\) To get the number of factors just add 1 to the powers and multiply (6+1) (2+1) = 7*3 ∴ z=7*3f(z)= (1+1)(1+1) = 2*2 = 4∵ \((7^1)(3^1)\) ∴ Answer B



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Re: The function f(n) for an integer n is defined as the number of
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28 May 2018, 07:29
Hey, guys. Thanks a lot, this way is much easier
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Re: The function f(n) for an integer n is defined as the number of
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15 May 2019, 11:13
this question seems to be tough question



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Re: The function f(n) for an integer n is defined as the number of
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15 May 2019, 11:51
nigina93 wrote: Hey, guys. Thanks a lot, this way is much easier How the answer can be B? yesterday it was C.



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Re: The function f(n) for an integer n is defined as the number of
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18 May 2019, 01:00
Manually finding factors are pretty time concuming method.



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Re: The function f(n) for an integer n is defined as the number of
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18 May 2019, 02:16
gmatjindi wrote: Manually finding factors are pretty time concuming method. gmatjindi  Unfortunately, thats the only way to solve this problem. The important takeaway in this problem is 1. Prime factorize number to the form \(a^x∗b^y∗c^z\) where a,b,c are the prime numbers. 2. Total number of prime factors can be calculated by using \((x+1)(y+1)(z+1)\)
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Re: The function f(n) for an integer n is defined as the number of
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20 May 2019, 14:13
Thank you very much for your detailed explanation!




Re: The function f(n) for an integer n is defined as the number of
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