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# How many terminating zeroes does 200! have? (A) 40 (B) 48

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How many terminating zeroes does 200! have? (A) 40 (B) 48 [#permalink]  07 Jul 2003, 05:25
How many terminating zeroes does 200! have?

(A) 40
(B) 48
(C) 49
(D) 55
(E) 64
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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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what is terminating?
GMAT Instructor
Joined: 07 Jul 2003
Posts: 770
Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE
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Kudos [?]: 57 [0], given: 0

Terminating in this context mean "placed at the end." For example, 1000 has 3 terminating zeroes, 1,000,000 has 6 terminating zeroes, and googol has 100 terminating zeroes.
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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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Express 200 as product of primes containing 2 and 5 , because each 2X5 produces one zero

total 2 and 5s in 200 = 200/5 + 200/25 = 40 + 8

So there must be 48 terminating zeroes in 200!
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Brainless

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You have the right idea. Close but no cigar.

Look again, is your analysis complete?
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Best,

AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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AkamaiBrah wrote:
You have the right idea. Close but no cigar.

Look again, is your analysis complete?

Did I miss one more factor containing 125 ( 200 / 5.5.5 ) = 1

So total it makes 49
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Brainless

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That is exactly correct.

In case you were wondering, 200! = 78865 78673 64790 50355 23632 13932 18506 22951 35977 68717 32632 94742 53324 43594 49963 40334 29203 04284 01198 46239 04177 21213 89196 38830 25764 27902 42637 10506 19266 24952 82993 11134 62857 27076 33172 37396 98894 39224 45621 45166 42402 54033 29186 41312 27428 29485 32775 24242 40757 39032 40321 25740 55795 68660 22603 19041 70324 06235 17008 58796 17892 22227 89623 70389 73747 20000 00000 00000 00000 00000 00000 00000 00000 00000 00000.
_________________

Best,

AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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Kudos [?]: 32 [0], given: 0

AkamaiBrah wrote:
That is exactly correct.

In case you were wondering, 200! = 78865 78673 64790 50355 23632 13932 18506 22951 35977 68717 32632 94742 53324 43594 49963 40334 29203 04284 01198 46239 04177 21213 89196 38830 25764 27902 42637 10506 19266 24952 82993 11134 62857 27076 33172 37396 98894 39224 45621 45166 42402 54033 29186 41312 27428 29485 32775 24242 40757 39032 40321 25740 55795 68660 22603 19041 70324 06235 17008 58796 17892 22227 89623 70389 73747 20000 00000 00000 00000 00000 00000 00000 00000 00000 00000.

i know it 49 but how did you calculate 200!? i donot think a general computer gives such a dianosure number.
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