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How many positive divisors does 6! have?

 Mar 19, 2019
 #1
avatar+140 
0

wouldn't it be 6 because 6! is 1*2*3*4*5*6

 Mar 19, 2019
 #2
avatar+111390 
0

A number factored into   primes   a^m * b^n .....     has  (m + 1) ( n + 1)...  positive divisors

 

6! =   720

 

Factor into primes

 

36 * 20  =

 

9 * 4 * 4 * 5  =

 

3^2 * 2^2 * 2^2 * 5  =

 

3^2 + 2^4 * 5^1

 

The number of positive divisors  =

 

(2 + 1) ( 4 + 1) (1 + 1 ) =

 

3 *   5  * 2  =

 

30 positive divisors

 

 

cool cool cool

 Mar 19, 2019
 #3
avatar+140 
0

thanks

CorbellaB.15  Mar 19, 2019

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