How many prime factors 100! has?

Question

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Bunuel · Answer

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.

shrive555 · Answer

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

krishnasty · Answer

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?

Bunuel · Answer

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.

sahilvijay · Answer

We know that there are 25 prime numbers between 1 to 100 => when 100! is written => 100x99x98x97..........x3x2x1 they will get repeated so 25 is the number of primes Answer choice B

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How many prime factors 100! has?

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How many prime factors 100! has?

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