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100!

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Senior Manager
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100! [#permalink] New post 02 Dec 2010, 08:34
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

17% (01:47) correct 83% (01:15) wrong based on 6 sessions
How many prime factors 100! has

24
25
27
29
31
[Reveal] Spoiler: OA

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Kudos [?]: 25070 [0], given: 2702

Re: 100! [#permalink] New post 02 Dec 2010, 08:42
Expert's post
shrive555 wrote:
How many prime factors 100! has

24
25
27
29
31


100!=1*2*3*...*100, so 100! has all prime factors which are less than 100 and only them. It happens to be that there are 25 primes less than 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.

Answer: B.

I really doubt that this is a realistic GMAT question: either you should remember the fact that there are 25 primes less than 100 or you should jut use brute force to count them.
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Senior Manager
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Posts: 333
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Kudos [?]: 59 [0], given: 193

Re: 100! [#permalink] New post 02 Dec 2010, 10:57
you're right B. i was going through the topic " finding the Number of powers of a prime number P in the n!" in Number Theory article and thought that we could find Number of prime factors in any factorial given through the formula n/p + n/p^2 ........till p^x < n
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Kudos [?]: 13 [0], given: 8

Re: 100! [#permalink] New post 03 Dec 2010, 01:56
Bunuel wrote:
shrive555 wrote:
How many prime factors 100! has

24
25
27
29
31


100!=1*2*3*...*100, so 100! has all prime factors which are less than 100 and only them. It happens to be that there are 25 primes less than 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.

Answer: B.

I really doubt that this is a realistic GMAT question: either you should remember the fact that there are 25 primes less than 100 or you should jut use brute force to count them.


Brunel, can we do this for every number?

for example, can we say that 55! would have as many prime number as the count of total prime numbers between 1 and 55?
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Re: 100! [#permalink] New post 03 Dec 2010, 02:03
Expert's post
krishnasty wrote:
Bunuel wrote:
shrive555 wrote:
How many prime factors 100! has

24
25
27
29
31


100!=1*2*3*...*100, so 100! has all prime factors which are less than 100 and only them. It happens to be that there are 25 primes less than 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.

Answer: B.

I really doubt that this is a realistic GMAT question: either you should remember the fact that there are 25 primes less than 100 or you should jut use brute force to count them.


Brunel, can we do this for every number?

for example, can we say that 55! would have as many prime number as the count of total prime numbers between 1 and 55?


Sure. 55!=1*2*3*...*55.

Now, as prime number cannot be written as a product of two factors, both of which are greater than 1 then prime more than 55 can not be a factor of 55! (prime more than 55, for example 71, just no way can occur in 55!).

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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. ,11 Mixed Questions, 12 Fresh Meat

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., 11 New DS set.


What are GMAT Club Tests?
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Re: 100!   [#permalink] 03 Dec 2010, 02:03
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