急!小四 整除法 既數!!!

2008-10-23 6:10 am
_ _ _ _ _ _ 7_



有一個8位數由1-8個數字組成,
已知第7個位數為 7,
數字不可重覆使用,(即只可用 1,2,3,4,5,6,8)
而這個8位數同時需符合以下....


請先找出合乎以下條件的數:

1) 頭1個數值可以被1整除
ans: 1 / 2/ 3/ 4/ 5/ 6/ 8

2)頭2個數可以被2整除
ans: 12/14/16/18/24/26/28/32/34/36/38.......

3)頭3個數可以被3整除
ans: 123/126/132/135/138/144/153/156/162......

4) 頭4個數可以被4整除
ans : ?

5)頭5個數可以被5整除
ans: ?

6) 頭6個數可以被6整除
ans: ?

7) 頭7個數可以被7整除
ans: ?

8) 這8個數可以被8整除
ans: ?



最後: 根據以上所得, 要符合以上8項,
請問這個8位數是什麼?




p.s. 可以簡單解釋一下運算方法嗎?
是否有什麼公式的?



十萬個感激!!!!!

thx!!

回答 (1)

2008-10-24 1:00 am
✔ 最佳答案
Result: 38165472

Possible value for each digit:

1st: 1, 3
2nd: 2,4,6,8
3rd: 1, 3
4th: 2,4,6,8
5th: 5 (only value end at 5, 0 can be divided by 5)
6th: 2,4,6,8
7th: 7
8th: 2,4,6,8

for number divided by 4, only last two digit need to be concerned
the 3rd and 4th digit together can also be divided by 4
so 4th:2,6

as 1-3 digit can be divided by 3 then 1-3 digit divided by 6 would have 0 or 3 reminder, so 3X5X or 0X5X should be divided by 6

3258, 3654, 258, 654, so 6th:4,8

for number divided by 8, only last three digit need to be concerned
5X7X --> 547X, 587X ->5472, 5872 can be divided by 8

so 8th: 2
then 4th:6
then 6th:4
then 2th:8

Finally try 1836547 and 3816547 divided by 7 and get the result

38165472
參考: me


收錄日期: 2021-04-15 19:15:10
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20081022000051KK02090

檢視 Wayback Machine 備份