Number Theory - all prime #'s that divide 50!

[Jamers328]

My problem is: Find all prime numbers that divide 50!.

I know I can use Corollary 1 from Thm 3.1, which states:
If p|a1, a2, ... an, then p|ai for some 1 <(or = to) i <(or = to) n.

 

[stapel]

Hint: What is the definition of "factorial"? In particular, what must be the factors of "50!"?

Eliz.

 

[Jamers328]

50! = 50x49x48x47x46........x3x2x1

The factors of 50! must be... any of those numbers 1-50???

:?

 

[stapel]

50! = 50x49x48x47x46........x3x2x1

The factors of 50! must be... any of those numbers 1-50?

Exactly, or products thereof.

But of course, since you're looking only for the prime factors, you couldn't care less about products, such as 100, being the product of the 50 and the 2. :lol:

So which are the prime factors of "50!"? :wink:

Eliz.

 

[Denis]

May I valiantly venture a guess that 11 may be one of them ?

 

[Jamers328]

yeah, definitely, thanks. I guess my teacher just wants us to do it a harder way? He said to include which result we are using to give our answer... like what method we are using. Thank you though!

 

[pka]