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If n is the greatest positive integer for which 2^n is a factor of 10!

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curtis0063
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If n is the greatest positive integer for which 2^n is a factor of 10! [#permalink] New post   25 Dec 2012, 10:05
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If n is the greatest positive integer for which 2^n is a factor of 10!, then n =?

A. 2
B. 4
C. 6
D. 8
E. 10

Is any one can provide a solution for this question?It's from GWD. Thanks!
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D
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Re: If n is the greatest positive integer for which 2^n is a factor of 10! [#permalink] New post   25 Dec 2012, 10:18
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In the questions where you are supposed to find out the maximum power of a prime factor which is a factor of n!, keep one only on thing in mind:
Let the prime number you are looking for be x, then:
\(n/x + n/x^2 + n/x^3.........n/x^k\) where \(x^k\) <=n.
If you apply this rule here,
\(10/2 +10/2^2 +10/2^3\) or 5+2+1=8.
Hence maximum power of 2 in \(10!\) will be 8.
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Re: If n is the greatest positive integer for which 2^n is a factor of 10! [#permalink] New post   14 May 2015, 23:06
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Hi All,

Many Test Takers get these types of questions wrong because they move too quickly through the work and don't do enough work on their pads. It's a relatively straight-forward prompt though...

We're essentially asked to find all the "2"s inside 10!

The 'key' to this question is to realize that some values have MORE THAN ONE 2 in them....

10! = (10)(9)(8)(7)(6)(5)(4)(3)(2)(1)

10 = 5x2 --> one 2
8 = 2x2x2 --> three 2s
6 = 3x2 --> one 2
4 = 2x2 --> two 2s
2 = 1x2 --> one 2

1+3+1+2+1 = eight 2s

Final Answer:
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D


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Re: If n is the greatest positive integer for which 2^n is a factor of 10! [#permalink] New post   26 Dec 2012, 03:49
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curtis0063 wrote:
If n is the greatest positive integer for which 2^n is a factor of 10!, then n =?

A. 2
B. 4
C. 6
D. 8
E. 10

Is any one can provide a solution for this question?It's from GWD. Thanks!


Check here: everything-about-factorials-on-the-gmat-85592.html
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Re: If n is the greatest positive integer for which 2^n is a factor of 10! [#permalink] New post   09 Jan 2014, 10:44
We can count the total number of powers of 2 in 10!
There are 8 of them.So answer D.

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Re: If n is the greatest positive integer for which 2^n is a factor of 10! [#permalink] New post   24 Mar 2016, 10:23
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curtis0063 wrote:
If n is the greatest positive integer for which 2^n is a factor of 10!, then n =?

A. 2
B. 4
C. 6
D. 8
E. 10

Is any one can provide a solution for this question?It's from GWD. Thanks!


\(\frac{10}{2}\) = 5
\(\frac{5}{2}\) = 2
\(\frac{2}{2}\) = 1

Now, 5+2+1 = 8

Hence the highest power of 2 that will divide 10! is 8
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Re: If n is the greatest positive integer for which 2^n is a factor of 10! [#permalink] New post   03 Apr 2018, 08:29
The answer must be D, i.e. 2 will be having a total power of 8 in 10!
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Re: If n is the greatest positive integer for which 2^n is a factor of 10! [#permalink] New post   05 Apr 2018, 17:12
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curtis0063 wrote:
If n is the greatest positive integer for which 2^n is a factor of 10!, then n =?

A. 2
B. 4
C. 6
D. 8
E. 10


Let’s put the even numbers from 2 to 10 in prime factors.

2

4 = 2^2

6 = 2 x 3

8 = 2^3

10 = 2 x 5

We see that there are 8 prime factors of 2 in 10!, so 8 is the value of n.

Alternate Solution:

We know that 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1. Let’s find all the 2’s in this product.

The number 10 contributes 1 two.

The number 8 contributes 3 twos.

The number 6 contributes 1 two.

The number 4 contributes 2 twos.

The number 2 contributes 1 two.

Thus, we have a total of 8 twos, and so 8 is the value of n..

Answer: D
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Re: If n is the greatest positive integer for which 2^n is a factor of 10! [#permalink] New post   28 Mar 2020, 05:30
curtis0063 wrote:
If n is the greatest positive integer for which 2^n is a factor of 10!, then n =?

A. 2
B. 4
C. 6
D. 8
E. 10

Is any one can provide a solution for this question?It's from GWD. Thanks!


Power of 2 in 10! = 5 + 2 + 1 = 8

IMO D
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Re: If n is the greatest positive integer for which 2^n is a factor of 10! [#permalink] New post   24 Apr 2021, 04:19
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Solution:

2 being a prime number, repeatedly divide the value by 2 and discard the remainder

Step 1- => 10 by 2 =5

=> 5 by 2 = 2 (Quotient =2 and remainder to be discarded)

=> 2 by 2 = 1 (Quotient =1 remainder to be discarded)

=> 1 by 2 = 0 (Quotient =0)

Step 2-Now add all these quotients from step 1 => 5+2+1 = 8 (option d)

Note:- You cannot divide by non prime numbers in this way, you may have to group them or count separately for the different factors.
For ex,if you have to count number of 6,count number of 3 s and 2s,observe the value which is smaller and that is your answer.

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Re: If n is the greatest positive integer for which 2^n is a factor of 10! [#permalink] New post   30 Jul 2023, 04:14
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