We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+2
55
1
avatar+290 

A certain positive integer has exactly 20 positive divisors.

a) What is the smallest number of primes that could divide the integer?

b) What is the largest number of primes that could divide the integer?

 Mar 22, 2019
 #1
avatar+99441 
+1

a)  We could have two primes that divide the integer 

Suppose that the number can be prime-factored into  a^m * b^n

So

(m + 1) ( n + 1)  =  20

And  m, n    could be  (in some order)   

3, 4  or

1, 9

 

b )   We could have three primes that divide the integer

Suppose that the integer  can be prime-factored into  a^k * b *m * c ^n

So

(k + 1) (m + 1) ( n + 1)  = 20

And k, m, n   could be  (in some order)

1, 1, 4

 

 

cool cool cool

 Mar 22, 2019

17 Online Users

avatar
avatar