SOLUTION: Hi tutors, I have a question. May I know how to solve this: Find all primes that divide 50! ? If it is 50, I have no problem but 50! is too large. Thank you.

Question 130014: Hi tutors,
I have a question. May I know how to solve this:
Find all primes that divide 50! ?
If it is 50, I have no problem but 50! is too large.
Thank you.
Found 2 solutions by solver91311, jim_thompson5910:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Every integer less than or equal to 50 is a factor of 50!, so every prime less than 50 is a factor. No prime larger than 50 can be a factor of 50! because it wouldn't be a factor of any of the factors of 50! Therefore, the answer is all primes less than 50. You can look up a table of primes several places on the web.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First expand 50!

50!=50*49*48*47*46*...*3*2*1

Notice how 50! is made of the product of the numbers from 1 to 50, including the prime numbers from 1 to 50. So the prime numbers:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47,

are factors of the prime numbers that make up 50! and are factors of the composite numbers that make up 50! (for example 4=2*2, 24=2*2*2*3, and 32=2*2*2*2*2). Remember, any number can be represented as a product of primes.

So to find the number of primes that divide into 50!, simply count the number of primes from 1 to 50.

So there are 15 primes that divide into 50!

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