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# What is the greatest value of x such that 10^x is a factor of 20! ?

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What is the greatest value of x such that 10^x is a factor of 20! ?  [#permalink]

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27 Dec 2016, 09:02
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Difficulty:

25% (medium)

Question Stats:

70% (00:59) correct 30% (01:06) wrong based on 105 sessions

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What is the greatest value of x such that 10^x is a factor of 20! ?

A. 1
B. 2
C. 3
D. 4
E. 5

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Re: What is the greatest value of x such that 10^x is a factor of 20! ?  [#permalink]

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27 Dec 2016, 11:00
Bunuel wrote:
What is the greatest value of x such that 10^x is a factor of 20! ?

A. 1
B. 2
C. 3
D. 4
E. 5

As 10^x=2^x*5^x
thus no. of 5's determine 10's in 20!
20/5=4

thus x=4

Ans D
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Re: What is the greatest value of x such that 10^x is a factor of 20! ?  [#permalink]

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27 Dec 2016, 11:16
Bunuel wrote:
What is the greatest value of x such that 10^x is a factor of 20! ?

A. 1
B. 2
C. 3
D. 4
E. 5

10 = 2*5

The highest value of 2 in 20! will be - 18

20/2 = 10
10/2 = 5
5/2 = 2
2/2 = 1

The highest value of 5 in 20! will be - 4

20/5 = 4

Since, there are fewer 5's than 2 , the greatest value of x such that 10^x is a factor of 20! will be x = 4

Hence, correct answer will be (D) 4

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Re: What is the greatest value of x such that 10^x is a factor of 20! ?  [#permalink]

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12 Jul 2017, 03:28
question is how many zeros in 20!

20/5=4

D
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Re: What is the greatest value of x such that 10^x is a factor of 20! ?  [#permalink]

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12 Jul 2017, 05:17
Bunuel wrote:
What is the greatest value of x such that 10^x is a factor of 20! ?

A. 1
B. 2
C. 3
D. 4
E. 5

{20/5} = 4
{20/25} = 0

So greatest value of x = 4

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Re: What is the greatest value of x such that 10^x is a factor of 20! ?  [#permalink]

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16 Jul 2017, 17:22
Bunuel wrote:
What is the greatest value of x such that 10^x is a factor of 20! ?

A. 1
B. 2
C. 3
D. 4
E. 5

We need to determine the maximum value for x such that 20!/10^x = integer.

We first need to determine how many 10s are contained in 20! We see that 10 breaks down to prime factors of 5 and 2, and since we know there are fewer 5s than 2s in 20!, we can find the number of 5s and thus be able to determine the number of times 10 divides 20!.

Recall that 20! = 20 x 19 x 18 x 17 x 16 x 15 x … x 2 x 1. Notice that there are only four numbers in 20! that have 5 as a factor: 20, 15, 10, and 5. Thus, we have a total of four 5s in 20!. This also means that 10 can divide into 20! no more than 4 times.

Therefore, the maximum value for x is 4.

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Re: What is the greatest value of x such that 10^x is a factor of 20! ?   [#permalink] 16 Jul 2017, 17:22
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