Converting from Base 10 to Base 6 Problems, 2

Category: Arithmetic

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Convert 148506 into Base 6.
  
Solution:
                                      
The given number which is 148506 is written in Base 10. 148506 can also be written as 148506₁₀. If you don't see any subscript at the given number, then that number is written in Base 10. Base 10 number is also called decimal system.  The digits of Base 10 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Base 10 number is a common number that we are using right now in everyday life. 
   
On the other hand, Base 6 number is a number whose digits are 0, 1, 2, 3, 4, and 5. If you see a subscript of 6 at the given number, then that number is written in Base 6. Base 6 number is also called heximal system. 
      
Now, let's convert 148506 into Base 6. How? Let's divide 148506 by 6 as follows:
   
                148506 ÷ 6 = 24751 + R(0)
   
Next, let's divide the quotient, which is 24751, as follows: 
    
                148506 ÷ 6 = 24751 + R(0)
                  24751 ÷ 6 =   4125 + R(1)
 
Do the same thing with 4125 until the quotient is 0 as follows:
   
                 148506 ÷ 6 = 24751 + R(0)
                   24751 ÷ 6 =   4125 + R(1) 
                     4125 ÷ 6 =     687 + R(3) 
                       687 ÷ 6 =     114 + R(3) 

                       114 ÷ 6 =       19 + R(0)

                         19 ÷ 6 =         3 + R(1)

                           3 ÷ 6 =         0 + R(3)

                  
The remainders will be the digits of Base 6 number. Use the digits of the remainders from bottom to top. Therefore,
   
                  148506 = 3103310₆