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If 60! is written out as an integer, with how many [#permalink]
 26 Sep 2010, 13:11
Question Stats:
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23% (00:38) wrong based on 11 sessions
If 60! is written out as an integer, with how many consecutive 0’s will that integer end? A. 6 B. 12 C. 14 D. 42 E. 56
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Re: How many zeroes at the end of 60!? [#permalink]
26 Sep 2010, 13:15
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Orange08 wrote: If 60! is written out as an integer, with how many consecutive 0’s will that integer end?
6
12
14
42
56 Trailing zeros:Trailing zeros are a sequence of 0's in the decimal representation (or more generally, in any positional representation) of a number, after which no other digits follow. 125000 has 3 trailing zeros; The number of trailing zeros in the decimal representation of n!, the factorial of a non-negative integer n, can be determined with this formula: \frac{n}{5}+\frac{n}{5^2}+\frac{n}{5^3}+...+\frac{n}{5^k}, where k must be chosen such that 5^(k+1)>nIt's more simple if you look at an example: How many zeros are in the end (after which no other digits follow) of 32!? \frac{32}{5}+\frac{32}{5^2}=6+1=7 (denominator must be less than 32, 5^2=25 is less) So there are 7 zeros in the end of 32! The formula actually counts the number of factors 5 in n!, but since there are at least as many factors 2, this is equivalent to the number of factors 10, each of which gives one more trailing zero. BACK TO THE ORIGINAL QUESTION:According to above 60! has \frac{60}{5}+\frac{60}{25}=12+2=14 trailing zeros. Answer: C. For more on this issues check Factorials and Number Theory links in my signature. Hope it helps.
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Re: How many zeroes at the end of 60!? [#permalink]
26 Sep 2010, 13:17
Many thanks.
silly question probably - can real test contain such question?
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Re: How many zeroes at the end of 60!? [#permalink]
26 Sep 2010, 13:21
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MGMAT Factorial 700+? [#permalink]
19 Jan 2011, 13:31
Is there a mathmatical approach to this? If 60! is written out as an integer, with how many consecutive 0’s will that integer end? a)6 b)12 c)14 d)42 e)56 Posted from my mobile device 
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Re: MGMAT Factorial 700+? [#permalink]
19 Jan 2011, 13:57
devide 60! by a 5 as follows:
60/5 + 60/5^2 + .....= 14
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Re: MGMAT Factorial 700+? [#permalink]
19 Jan 2011, 14:11
shashankp27 wrote: devide 60! by a 5 as follows:
60/5 + 60/5^2 + .....= 14 Could you explain that a bit more? because 60/5 is 12, and adding 60/5^2 will be 14.4, so going further will result in an even larger number. Also why a 5? Posted from my mobile device
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Re: MGMAT Factorial 700+? [#permalink]
19 Jan 2011, 14:20
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During the test I would simply write down all the numbers between 1 and 60 that end with a 5 or a 0 (5*2 = 10), so we will have: 5, 10 , 15 , 20, 25 (5*5), 30, 35, 40, 45, 50 (5*5*2) , 55, 60. If we count all the numbers we will get 12, BUT we need to remember that 25 = 5*5 so we have 2 zeros and 50 = 5*5*2 so we have 2 more. Therefore, the correct answer is C - 14.
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Re: MGMAT Factorial 700+? [#permalink]
19 Jan 2011, 19:13
Whenever you want to find the number of zeros in a N! then do the following :
devide N by 5 such that
(N/5) + (N/5^2) + (N/5^3) + ..... unless 5^p where p= 1, 2,3 ... is more than N ..
Eg : let's say you want to find the number of Zero's in 125! so
divide 125/5 = 25 then
divide 125/5^2 =125/25= 5 then
divide 125/5^3= 125/125=1 ,
so a total of 25 +5+1 trailing zeros will be present. Always consider the rounded figures .In the original example :
60/5 = 12
60/5^2 = 60/25=2.4 , however you are not concerned with the decimal values here, so take this as 2
next would be 60/5^3 = 60/125 , so this would be (.some number) so stop your division here.
Whenever the denominator exceeds numerator , stop the process. Add the values to get the answer.
what would you do if the question asks to find the maximum power of 3 in 50! ?
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Re: MGMAT Factorial 700+? [#permalink]
20 Jan 2011, 02:53
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Re: MGMAT Factorial 700+? [#permalink]
20 Jan 2011, 06:22
shashankp27 wrote: Whenever you want to find the number of zeros in a N! then do the following :
devide N by 5 such that
(N/5) + (N/5^2) + (N/5^3) + ..... unless 5^p where p= 1, 2,3 ... is more than N ..
Eg : let's say you want to find the number of Zero's in 125! so
divide 125/5 = 25 then
divide 125/5^2 =125/25= 5 then
divide 125/5^3= 125/125=1 ,
so a total of 25 +5+1 trailing zeros will be present. Always consider the rounded figures .In the original example :
60/5 = 12
60/5^2 = 60/25=2.4 , however you are not concerned with the decimal values here, so take this as 2
next would be 60/5^3 = 60/125 , so this would be (.some number) so stop your division here.
Whenever the denominator exceeds numerator , stop the process. Add the values to get the answer.
what would you do if the question asks to find the maximum power of 3 in 50! ? Ok I understand the trailing zeros now. Ignoring the decimal helps, I was just adding. Make more sense thank you for the explanation. Maximum power of 3 in 50!? Find the multiples of 3 from 1 to 50. Add them up. 3^21? Posted from my mobile device
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Re: How many zeroes at the end of 60!? [#permalink]
08 May 2012, 03:04
Bunuel wrote: Orange08 wrote: If 60! is written out as an integer, with how many consecutive 0’s will that integer end?
6
12
14
42
56 Trailing zeros:Trailing zeros are a sequence of 0's in the decimal representation (or more generally, in any positional representation) of a number, after which no other digits follow. 125000 has 3 trailing zeros; The number of trailing zeros in the decimal representation of n!, the factorial of a non-negative integer n, can be determined with this formula: \frac{n}{5}+\frac{n}{5^2}+\frac{n}{5^3}+...+\frac{n}{5^k}, where k must be chosen such that 5^(k+1)>nIt's more simple if you look at an example: How many zeros are in the end (after which no other digits follow) of 32!? \frac{32}{5}+\frac{32}{5^2}=6+1=7 (denominator must be less than 32, 5^2=25 is less) So there are 7 zeros in the end of 32! The formula actually counts the number of factors 5 in n!, but since there are at least as many factors 2, this is equivalent to the number of factors 10, each of which gives one more trailing zero. BACK TO THE ORIGINAL QUESTION:According to above 60! has \frac{60}{5}+\frac{60}{25}=12+2=14 trailing zeros. Answer: C. For more on this issues check Factorials and Number Theory links in my signature. Hope it helps. a question Bunuel (just for sure): 32/25 is 1.28 ....BUT if the result was for instance a number / another number = 1,764 we round it to 2 (the next integer) ?? I hope to be clear with my question .....
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Re: How many zeroes at the end of 60!? [#permalink]
08 May 2012, 11:03
carcass wrote:
a question Bunuel (just for sure): 32/25 is 1.28 ....BUT if the result was for instance a number / another number = 1,764 we round it to 2 (the next integer) ??
I hope to be clear with my question .....
no. U can check it say we have 29! 29/5 -29/25=5+1=6 now check it for sure 29 has 25 (two 5's); 20 (one 5); 15(one 5);10(one 5);5(one 5) total 5^6
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Re: How many zeroes at the end of 60!? [#permalink]
08 May 2012, 11:15
Bunuel wrote: Orange08 wrote: If 60! is written out as an integer, with how many consecutive 0’s will that integer end?
6
12
14
42
56 Trailing zeros:Trailing zeros are a sequence of 0's in the decimal representation (or more generally, in any positional representation) of a number, after which no other digits follow. 125000 has 3 trailing zeros; The number of trailing zeros in the decimal representation of n!, the factorial of a non-negative integer n, can be determined with this formula: \frac{n}{5}+\frac{n}{5^2}+\frac{n}{5^3}+...+\frac{n}{5^k}, where k must be chosen such that 5^(k+1)>nIt's more simple if you look at an example: How many zeros are in the end (after which no other digits follow) of 32!? \frac{32}{5}+\frac{32}{5^2}=6+1=7 (denominator must be less than 32, 5^2=25 is less) So there are 7 zeros in the end of 32! The formula actually counts the number of factors 5 in n!, but since there are at least as many factors 2, this is equivalent to the number of factors 10, each of which gives one more trailing zero. BACK TO THE ORIGINAL QUESTION:According to above 60! has \frac{60}{5}+\frac{60}{25}=12+2=14 trailing zeros. Answer: C. For more on this issues check Factorials and Number Theory links in my signature. Hope it helps. Hello Brunuel Thanks for this great answer but I am not familiar at all with trailing zeros How did you determined the limit to raise the power up to K ? how did you get the K BEST regards keiraria
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Re: How many zeroes at the end of 60!? [#permalink]
08 May 2012, 11:18
keiraria wrote: Hello Brunuel
Thanks for this great answer
but I am not familiar at all with trailing zeros
How did you determined the limit to raise the power
up to K ? how did you get the K
BEST regards
keiraria see the link below - http://gmatclub.com/forum/everything-about-factorials-on-the-gmat-85592.html
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Re: How many zeroes at the end of 60!? [#permalink]
09 May 2012, 01:05
carcass wrote: Bunuel wrote: Orange08 wrote: If 60! is written out as an integer, with how many consecutive 0’s will that integer end?
6
12
14
42
56 Trailing zeros:Trailing zeros are a sequence of 0's in the decimal representation (or more generally, in any positional representation) of a number, after which no other digits follow. 125000 has 3 trailing zeros; The number of trailing zeros in the decimal representation of n!, the factorial of a non-negative integer n, can be determined with this formula: \frac{n}{5}+\frac{n}{5^2}+\frac{n}{5^3}+...+\frac{n}{5^k}, where k must be chosen such that 5^(k+1)>nIt's more simple if you look at an example: How many zeros are in the end (after which no other digits follow) of 32!? \frac{32}{5}+\frac{32}{5^2}=6+1=7 (denominator must be less than 32, 5^2=25 is less) So there are 7 zeros in the end of 32! The formula actually counts the number of factors 5 in n!, but since there are at least as many factors 2, this is equivalent to the number of factors 10, each of which gives one more trailing zero. BACK TO THE ORIGINAL QUESTION:According to above 60! has \frac{60}{5}+\frac{60}{25}=12+2=14 trailing zeros. Answer: C. For more on this issues check Factorials and Number Theory links in my signature. Hope it helps. a question Bunuel (just for sure): 32/25 is 1.28 ....BUT if the result was for instance a number / another number = 1,764 we round it to 2 (the next integer) ?? I hope to be clear with my question ..... We take into account only the quotient of the division, that is 32/5=6. keiraria wrote: Hello Brunuel
Thanks for this great answer
but I am not familiar at all with trailing zeros
How did you determined the limit to raise the power
up to K ? how did you get the K
BEST regards
keiraria The last denominator (5^2) must be less than numerator (60). Hope it's clear.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!
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MGMAT CAT question [#permalink]
20 May 2012, 14:35
If 60! is written out as an integer, with how many consecutive 0’s will that integer end?
a) 6
b) 12
c) 14
d) 42
e) 56
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Re: MGMAT CAT question [#permalink]
20 May 2012, 14:40
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Re: How many zeroes at the end of 60!? [#permalink]
20 May 2012, 21:03
Bunuel wrote: Orange08 wrote: If 60! is written out as an integer, with how many consecutive 0’s will that integer end?
6
12
14
42
56 Trailing zeros:Trailing zeros are a sequence of 0's in the decimal representation (or more generally, in any positional representation) of a number, after which no other digits follow. 125000 has 3 trailing zeros; The number of trailing zeros in the decimal representation of n!, the factorial of a non-negative integer n, can be determined with this formula: \frac{n}{5}+\frac{n}{5^2}+\frac{n}{5^3}+...+\frac{n}{5^k}, where k must be chosen such that 5^(k+1)>nIt's more simple if you look at an example: How many zeros are in the end (after which no other digits follow) of 32!? \frac{32}{5}+\frac{32}{5^2}=6+1=7 (denominator must be less than 32, 5^2=25 is less) So there are 7 zeros in the end of 32! The formula actually counts the number of factors 5 in n!, but since there are at least as many factors 2, this is equivalent to the number of factors 10, each of which gives one more trailing zero. BACK TO THE ORIGINAL QUESTION:According to above 60! has \frac{60}{5}+\frac{60}{25}=12+2=14 trailing zeros. Answer: C. For more on this issues check Factorials and Number Theory links in my signature. Hope it helps. Thanks for the detailed explanation... new cocnept for me 
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Re: How many zeroes at the end of 60!?
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20 May 2012, 21:03
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