SOLUTION: convert 287 to base 3

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Question 727402: convert 287 to base 3
Found 2 solutions by KMST, Edwin McCravy:
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Dividing 287 by 3 we get 95 for a quotient and highlight%28remainder=red%282%29%29.
Dividing 95 by 3 we get 31 for a quotient and highlight%28remainder=green%282%29%29.
Dividing 31 by 3 we get 10 for a quotient and highlight%28remainder=red%281%29%29.
Dividing 10 by 3 we get 3 for a quotient and highlight%28remainder=blue%281%29%29.
Dividing 3 by 3 we get highlight%28green%281%29%29 for a quotient and highlight%28remainder=0%29.

The answer is highlight%28101122%29=green%281%290blue%281%29red%281%29green%282%29red%282%29%29 in base 3, whose value is


The reason why the repeated division works can be explained through that example like this
The last division tells us that
red%283%29=3%2Agreen%281%29%2B0 because 3 ÷ 3 = 1 R0
The previous division tells us that
10=3%2Ared%283%29%2Bblue%281%29 because 10 ÷ 3 = 3 R1
Putting them both together
10=3%2A%283%2Agreen%281%29%2B0%29%2Bblue%281%29=green%281%29%2A3%5E2%2B0%2A3%2Bblue%281%29
The division before that told us that
31=3%2A10%2Bred%281%29 and that along with
10=green%281%29%2A3%5E2%2B0%2A3%2Bblue%281%29 gets us
31=3%28green%281%29%2A3%5E2%2B0%2A3%2Bblue%281%29%29%2Bred%281%29=green%281%29%2A3%5E3%2B0%2A3%5E2%2Bblue%281%29%2A3%2Bred%281%29
The second division told us that
95=3%2A31%2Bgreen%282%29 and that along with
31=green%281%29%2A3%5E3%2B0%2A3%5E2%2Bblue%281%29%2A3%2Bred%281%29 gets us
95=3%2A%28green%281%29%2A3%5E3%2B0%2A3%5E2%2Bblue%281%29%2A3%2Bred%281%29%29%2Bgreen%282%29=
green%281%29%2A3%5E4%2B0%2A3%5E3%2Bblue%281%29%2A3%5E2%2Bred%281%29%2A3%2Bgreen%282%29
The first division told us that
287=3%2A95%2Bred%282%29 and that along with
95=green%281%29%2A3%5E4%2B0%2A3%5E3%2Bblue%281%29%2A3%5E2%2Bred%281%29%2A3%2Bgreen%282%29 gets us
which means

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
287 to base 3
We divide 3 into 287, getting 95 with remainder 2. We write the 
quotient 95 below and the remainder 2 out to the side, like this:

3)287
   95 R=2

Under that, we divide 3 into 95, getting 31 with remainder 2. We 
write the quotient 31 below and the remainder 2 out to the side, 
like this:

3)287
 3)95 R=2
   31 R=2
  
Under that, we divide 3 into 31, getting 10 with remainder 1.  We
write the quotient 10 below and the remainder 1 out to the side,
like this:

3)287
 3)95 R=2
 3)31 R=2
   10 R=1

Under that, we divide 3 into 10, getting 13 with remainder 1.  We
write the quotient 3 below and the remainder 1 out to the side,
like this:

3)287
 3)95 R=2
 3)31 R=2
 3)10 R=1
    3 R=1

Under that, we divide 3 into 3, getting 1 with remainder 0.  We
write the quotient 1 below and the remainder 0 out to the side,
like this:

3)287
 3)95 R=2
 3)31 R=2
 3)10 R=1
  3)3 R=1
    1 R=0
   
Under that, we divide 3 into 1, getting 0 with remainder 1.  We
write the quotient 0 below and the remainder 1 out to the side,
like this:

3)287
 3)95 R=2
 3)31 R=2
 3)10 R=1
  3)3 R=1
  3)1 R=0
    0 R=1

We are done since the last quotient was 0.

To get the number 287 in base 3, we write
the remainders from bottom to top:

287 in base ten equals 101122 in base 3.

Edwin