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Find the largest prime number (in decimal form) that divides the sum, 

MIRB16  Apr 7, 2018
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 #1
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nvm got it!

MIRB16  Apr 7, 2018
 #2
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1_2 + 10_2 + 100_2 + 1000_2 +10000_2 +100000_2 + 1000000_2 + 10000000_2 + 100000000_2=?

 

=111111111_2 . Count the number of 1s from right to left and you get 9 "1s", from 0 to 8 as powers of 2 as follows. Start from left to right:

2^8 + 2^7 + 2^6 + 2^5 + 2^4 + 2^3 + 2^2 + 2^1 + 2^0 =

256 + 128 + 64 +  32   +   16  +  8   +  4   +   2   +   1  =511 in base 10. And since:

511 = 7 * 73. As you can see, the largest prime that will divide 511 is 73.

Guest Apr 7, 2018

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