GWD_Total31: 01 Math Q.4

[piyopiyo]

Q4:
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

Ans: D

Dear all,

I have no idea how to solve this problem .... What is the best way to solve this problem??

Thank you very much!!!

[vantreal]

greatest integer k 有點confusing,
(不知像是說 greatest value of k 還是 greatest number of k)

我的解讀是 greatest number of k.

n= 1 x 2 x 3 x 4......x 20
= 1 x (2x1) x 3 x (2x2) x ...........x (2x2x5)
= (2k) x (某數) <-題目給的條件

所以k可以有18種數字 (from 1 to 18)
(直接數2出現的次數就可以了)

[lucyyeh]

閣下真是高明，在請教一下，為什麼不能把20算進去?謝謝!

[vantreal]

閣下真是高明，在請教一下，為什麼不能把20算進去?謝謝!

哈哈哈, 我一點都不高明 ~~
(同個讀書會的還這麼客氣 )

有阿, 我有把20算進去.
(剛剛有修改了一下答案, 寫的不達意, 歹勢~)

[FIG]

Q4:
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 n?

請問一下，題目是否是問" 2^k is a factor of n?"

[vantreal]

Q4:
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 n?

請問一下，題目是否是問" 2^k is a factor of n?"

哈哈, 這也是我的assumption

[FIG]

那我總算看懂了..:)

[piyopiyo]

Thank you very much, vantreal~~~!!!! You are great!

I'm sorry. I did have a typo. It should be 2^k instead of 2k...

Thank you~