December 14, 2018 December 14, 2018 09:00 AM PST 10:00 AM PST 10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners. December 14, 2018 December 14, 2018 10:00 PM PST 11:00 PM PST Carolyn and Brett  nicely explained what is the typical day of a UCLA student. I am posting below recording of the webinar for those who could't attend this session.
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If 12!/3^x is an integer, what is the greatest possible value of x?
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28 Feb 2016, 08:13
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Re: If 12!/3^x is an integer, what is the greatest possible value of x?
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28 Feb 2016, 12:19
Bunuel wrote: If 12!/3^x is an integer, what is the greatest possible value of x?
A. 3 B. 4 C. 5 D. 6 E. 7 12  4*3 9  3*3 6  2*3 3  1*3 Hence max of 3^5 is allowed. IMO C. This is not the right way of doing. Forgot the easy approach. Will update.



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Re: If 12!/3^x is an integer, what is the greatest possible value of x?
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28 Feb 2016, 15:18
Bunuel wrote: If 12!/3^x is an integer, what is the greatest possible value of x?
A. 3 B. 4 C. 5 D. 6 E. 7 This question is asking how many power of 3 exists in 12! easiest way is to identify factor of three 12 > 4*3 => 1 power of 3 9 > 3*3=> 2 power of 3 6 > 2*3=> 1 power of 3 3 > 1*3=> 1 power of 3 Total equal 5 hence C



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Re: If 12!/3^x is an integer, what is the greatest possible value of x?
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29 Oct 2016, 07:52
12/3 + 12/9 = 4 + 1 = 5
3^5



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Re: If 12!/3^x is an integer, what is the greatest possible value of x?
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29 Oct 2016, 10:32
Bunuel wrote: If 12!/3^x is an integer, what is the greatest possible value of x?
A. 3 B. 4 C. 5 D. 6 E. 7 12/3 = 4 4/3 = 1 4 + 1 = 5 Hence correct answer will be (C) 5
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Re: If 12!/3^x is an integer, what is the greatest possible value of x?
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27 Jun 2018, 07:58
Abhishek009 wrote: Bunuel wrote: If 12!/3^x is an integer, what is the greatest possible value of x?
A. 3 B. 4 C. 5 D. 6 E. 7 12/3 = 4 4/3 = 1 4 + 1 = 5 Hence correct answer will be (C) 5i didnt understand why you divided 4 by 3. please explain



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Re: If 12!/3^x is an integer, what is the greatest possible value of x?
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27 Jun 2018, 10:54
12=3*4 9=3*3 6=3*2 3
Answer C. count of 3 s



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Re: If 12!/3^x is an integer, what is the greatest possible value of x?
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28 Jun 2018, 15:23
Abhishek009 wrote: Bunuel wrote: If 12!/3^x is an integer, what is the greatest possible value of x?
A. 3 B. 4 C. 5 D. 6 E. 7 12/3 = 4 4/3 = 1 4 + 1 = 5 Hence correct answer will be (C) 5Kindly specify dividing 4 by 3 by the same shortcut method that you have applied in the tagged answer. i have got the factorisation concept. thanks. regards.



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If 12!/3^x is an integer, what is the greatest possible value of x?
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30 Jun 2018, 13:16
Bunuel wrote: If 12!/3^x is an integer, what is the greatest possible value of x?
A. 3 B. 4 C. 5 D. 6 E. 7 This question is easy, and a good way to demonstrate one way to find the number of "powers of a prime in \(n!\)." (See footnote.*) This \(n!\) is small. Most will not be. The method: Divide \(n=12\) (without !) by increasing powers of \(3\). Don't worry about remainders. (1) 12 divided by \(3^1:(\frac{12}{3^1})=4\) (2) 12 divided by \(3^2: (\frac{12}{3^2})=(\frac{12}{9})=1\) (3) 12 divided by \(3^3=27\): Will not work. \(\frac{12}{27}<1\) (4) Add up the results of division by each power of 3 that "worked": \((4 + 1) = 5\) There are 5 powers of 3 in 12!, so the greatest possible value of \(x=5\) Answer C *The theory is described by Bunuel in Everything About Factorials, Finding the Number of Powers of a Prime, p, in the n!, here. Important! The post also has an example.



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If 12!/3^x is an integer, what is the greatest possible value of x?
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30 Jun 2018, 13:16
ankurkshl wrote: Abhishek009 wrote: Bunuel wrote: If 12!/3^x is an integer, what is the greatest possible value of x?
A. 3 B. 4 C. 5 D. 6 E. 7 12/3 = 4 4/3 = 1 4 + 1 = 5 Hence correct answer will be (C) 5Kindly specify dividing 4 by 3 by the same shortcut method that you have applied in the tagged answer. i have got the factorisation concept. thanks. regards. ankurkshl , the method is one way to find the number of powers of a prime number in \(n!\). Divide \(n\) (without the !) by the prime number (here, 3). \(n=12\) Use the resulting quotient as your new dividend, and divide again by \(3\) until the resulting number is too small to divide by \(3\) 1) 12 divided by 3: \(\frac{12}{3^1}=4\) 2) Now use \(4\), and divide by 3. Do not worry about remainders.* \(\frac{4}{3}=1\) 3) Sum the number of 3s from all stages: (4 + 1) = 5 There are five factors of 3 in 12!, so the greatest possible value for x is 5. Answer C Hope that helps. * We just need to know whether \(4\) can be divided by \(3\) such that the result \(\geq1\) (How many times does 3 go into 4? One time, with a remainder about which we do not care). This method is a variation on the method I posted above. Both are VERY handy when n! is huge.



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Re: If 12!/3^x is an integer, what is the greatest possible value of x?
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02 Jul 2018, 09:03
Bunuel wrote: If 12!/3^x is an integer, what is the greatest possible value of x?
A. 3 B. 4 C. 5 D. 6 E. 7 o determine the number of factors of 3 within 12!, we can use the following shortcut in which we divide 12 by 3, and then divide the quotient of 12/3 by 3 and continue this process until we can no longer get a nonzero integer as the quotient. 12/3 = 4 4/3 = 1 (we can ignore the remainder) Since 1/3 does not produce a nonzero quotient, we can stop. The final step is to add up our quotients; that sum represents the number of factors of 3 within 12!. Thus, there are 4 + 1 = 5 factors of 3 within 12!. Thus, the greatest value of x is 5. Answer: C
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