+0  
 
0
79
6
avatar+102 

What is the smallest whole number b  such that 62 can be expressed in base b using only three digits?
Not only I am asking for the answer to this problem, can you guys please tell me how to convert out of base 10? (I don't know how to)

 Feb 4, 2021
edited by vockeyvockvock  Feb 4, 2021
 #1
avatar+31703 
+3

Like so

 Feb 4, 2021
 #2
avatar+102 
+1

Thanks a lot!

vockeyvockvock  Feb 4, 2021
 #3
avatar+116125 
+2

Converting out of  base 10

 

Using  the base that Alan found    62  base 10  to Base 4

 

62 / 4  =    15   +  Remainder  2

 

15  / 4   =   3   +  Remainder  3

 

3  / 4  =   0  +  Remainder    3               

 

We stop  when the division  produces a whole number  of  0

 

Read  the remainders  "backwards"  from  bottom to top  = 

 

3324  

 

 

 

cool cool cool

 Feb 4, 2021
 #4
avatar+102 
+1

So that would mean 356 in base 10 to base 8 is

356 / 8 = 44 + remainder 4

44 / 8 = 5 + remainder 4

4 / 8 = 0 + remainder 4

So 356 converted is 444?

@cphil

vockeyvockvock  Feb 4, 2021
edited by vockeyvockvock  Feb 4, 2021
 #5
avatar+73 
0

yes, Vockey, i think that is right! :)

macar0ni  Feb 4, 2021
 #6
avatar+116125 
+1

356  to  Base  8

 

356  / 8   =  44  +  R 4

44/8  =       5  +  R4

5/ 8    =     0  + R5

 

5(8)^2  + 4(8)  + 4  =

 

5 (64)  + 32  + 4  =

 

320 + 32  + 4   =

 

356   !!!

 

So   5448

 

 

cool cool  cool

CPhill  Feb 4, 2021

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