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In base 6, the place positions are 7776s, 1296s, 216s, 36s, 6s, and 1s.
First, determine the number of 1296s. There is 1 amount of 1296.
The remaining amount, which is 2009 - 1296, is 713.
713 / 216 is 3 plus a remainder, so there are 3 amounts of 216.
The remaining amount, which is 713 - (216 x 3), is 65.
65 / 36 is 1 plus a remainder, so there is 1 amount of 36.
The remaining amount, which is 65 - 36, is 29.
29 / 6 is 4 plus a remainder, so there are 4 amounts of 6.
The remaining amount, which is 29 - (6 x 4), is 5.
So, there are 5 amounts of 1.
Therefore, 2009 in base 6 is 13,145.
Doublecheck: (1 x 1296) + (3 x 216) + (1 x 36) + (4 x 6) + (1 x 5)
= 1296 + 648 + 36 + 24 + 5 = 2009
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∙ 15y ago
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