求助！求助！一题GWD数学

当当的驿站 · 发表于 2009-12-17 00:47:59

If n is the product of the integers from1 to 20 inclusive, what is the greatest integer k for which 2^k is a factor of n?

A. 10

B. 12

C. 15

D. 18

E. 20

求助！这题怎么解的啊谢谢大家！

okk · 发表于 2009-12-17 01:01:59

Divide 20 by increasing powers of 2 till u get 0 as the integer quotient and add all the integer quotients in the process

i.e

20/2 + 20/2 ^ 2 + 20 / 2 ^3 + 20/2 ^4 + 20 / 2^5

=20/2+20/4+20/8+20/16+20/32
= 10+5+2+1+0 (we stop here)

= 18

D)

当当的驿站 · 发表于 2009-12-17 01:05:04

谢谢谢谢！！！好人啊好人！谢谢！

求助！求助！一题GWD数学

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