+0  
 
0
120
4
avatar+77 

Find the base of the numeration system in which 135/21 has a zero remainder.

neurolover25  Feb 10, 2018
Sort: 

4+0 Answers

 #1
avatar
+1

If your 135/21 are ALREADY converted to the desired base, then:

135_7  mod  21_7 =0 remainder.

 

This does make sense, since 135_7 = 75_10, and 21_7 = 15_10. So, 75/15 =5 with no remainder.

Guest Feb 10, 2018
edited by Guest  Feb 10, 2018
edited by Guest  Feb 10, 2018
 #2
avatar+85620 
+1

This was answered by Melody a few days ago...I believe that she found the answer to be base 7 as follows:

 

[ 1b^2 + 3b  + 5 ]  / [ 2b + 1]     and when b  = 7 we have that

 

[ 7^2 + 3*7 + 5 ] / [ 2*7 + 1  ]  =

 

[ 49 + 21  + 5 ] / [ 15 ]

 

[ 70 + 5 ]  / [ 15]    =

 

[ 75] / [ 15]   =

 

5

 

 

cool cool cool

CPhill  Feb 10, 2018
edited by CPhill  Feb 11, 2018
 #3
avatar
0

Wow  !!  I didn't see Melody's answer, but that is very interesting way of doing it !!. So, you would arrive at the answer by trial and error? Or, is there a sure way of surmising the answer?

Guest Feb 10, 2018
 #4
avatar+85620 
0

She used trial and error....but..with the presence of the "5"  she knew that the base had to  be  6 or greater.......so...it didn't take her long to get to 7....LOL!!!!

 

 

cool cool cool

CPhill  Feb 11, 2018

10 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details