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What is the highest power of 2 dividing 1^1 * 2^2 * 3^3 *

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What is the highest power of 2 dividing 1^1 * 2^2 * 3^3 * [#permalink] New post 14 Apr 2006, 17:09
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What is the highest power of 2 dividing 1^1 * 2^2 * 3^3 * 4^4...15^15?

A. 56

B. 60

C. 63

D. 80

E. None of these
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 [#permalink] New post 14 Apr 2006, 18:09
What is the highest power of 2 dividing 1^1 * 2^2 * 3^3 * 4^4...15^15?

2^2
4^4 - (2^2)^4 = 2^8
6^6 - 2^6*3^6
8^8 - 2^24
10^10 - 2^10*5^10
12^12 - 2^24*3^12
14^14 - 2^14*7^14

So add them up, we get 88. Answer is E.
  [#permalink] 14 Apr 2006, 18:09
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What is the highest power of 2 dividing 1^1 * 2^2 * 3^3 *

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