GMAT数学题请说明理由哇Ifnistheproductoftheintegersfrom1to20inclusive,whatisthegreatestintegerkforwhich2kisafactorofA.\x0510B.\x0512C.\x0515D.\x0518E.\x0520我复制下来格式不对了原题不是2K是2的K次方

Question

GMAT数学题 请说明理由哇
If n is the product of the integers from1 to 20 inclusive,what is the greatest integer k for which 2k is a factor of
A.\x0510
B.\x0512
C.\x0515
D.\x0518
E.\x0520
我复制下来格式不对了 原题不是2K 是2的K次方 K是小的在2的右上角

Answer 1

D:
Just look for 2 as a factor in all the integers from 1 to 20,apparently,only even integers need to be considered:
2:1 (once)
4=2*2：2 (twice)
6:1 (once)
8 = 2*2*2:3 (3 times)
10:1 (once)
12=2*2*3:2 (twice)
14:1 (once)
16=2*2*2*2:4 (4 times)
18:1 (once)
20 = 2*2*5：2 (twice)
k = 1+2+1+3+1+2+1+4+1+2 = 18