2115 divided by 12 (all in base seven)

Question

I want the procedures in dividing 2115 by 12 (all in base seven)

Answer 1

One way to do this is to use long division in base 7.

To make it easier, we need multiples of 12₇ in base 7:

1×12=12

2×12=24

3×12=36

4×12=51 (4×2=7+1=11₇ so we carry 1; 4×1=4 plus carry = 51)

5×12=63 (5×2=7+3=13₇ so we carry 1; 5×1=5 plus carry = 63) or 51+12=63

6×12=105, that is, 63+12=105 (7 is 10₇)

         146

12 ) 2115

     - 12 (1×12)

         61

       - 51 (4×12)

         105

       - 105 (6×12)

            0 

ANSWER: 146 to base 7.

Another way is to convert to decimal: 12=7+2=9; 2115=2×343+49+7+5=686+61=747.

747/9=83=49+28+6=146₇.