+0  
 
0
57
1
avatar

Jan is thinking of a positive integer.  Her integer has exactly 16 positive factors, two of which are 12 and 15.  What is Jan's number?

 May 23, 2020
 #1
avatar+21945 
0

Jan is thinking of a positive integer.  Her integer has exactly 16 positive factors, two of which are 12 and 15.  What is Jan's number?

 

Factoring 12:  1 x 22 x 3

Factoring 15:  1 x 3 x 5

 

So, the number must have these factors:  22, 3, and 5.

 

22 x 3 x 5  =  60

60 has these factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60   --  12 factors, not 16.

 

So, let's try putting in another factor of 2:  60 x 2  =  120.

120 has these factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120   --  16 factors!

 May 23, 2020

10 Online Users