+0  
 
0
102
2
avatar

Compute the sum of all positive integers k for which the number k*1984*2 has exactly 21 positive divisors.

 Jun 20, 2021
 #1
avatar+179 
+2

To find divisors, we must prime factorize the number.  

 

1984*2 = 2^7 × 31

 

Using the divisor formula, however, we find that there is no integer value of k that this is true (8*2*(any integer) cannot = 21)

 

 

Because of this, there is no number that satisfies this, meaning the sum is 0

 

 

 

Additional material on the divisor formula I found on google is here: https://www.themathdoctors.org/counting-divisors-of-a-number/

 

 

Sidenote:  If there was no extra *2, then k=31 would make the number 1984*31 have 21 divisors.  

 Jun 20, 2021
edited by EnchantedLava68  Jun 20, 2021
 #2
avatar+2252 
0

Nice, I had the same idea but I thought that 0 was a very suspicious answer. 

 

=^._.^=

catmg  Jun 20, 2021

34 Online Users

avatar