請幫忙解解下列題目:
A three-digit number N leaves remainder 3 when divided by 7, remainder 5 when divided by 11 and remainder 8 when divided by 17. What is the number N?
A three-digit number N leaves remainder 3 when divided by 7, remainder 5 when divided by 11 and remainder 8 when divided by 17. What is the number N?
回應
訪客 (未驗證)
Re: 求救!!
2005-10-10 21:50N / 11 =?...........5
N / 17 =?...........8
請用孫子算法?再想想看! 我也再算........
sam
訪客 (未驗證)
Re: 求救!!
2005-10-10 22:2311 x 17 = 187, 187/7=26...5 ( 5不是他們要的,而是3)
5 x 2 =10 10/7=1.....3,
所以 11 x 17 x 2 = 374
======================
7, 17公倍數
7 x 17 = 119, 119/11=10...9
9 x 3 = 27, 27/11=2...5,
所以17x 7 x 3 = 357
=======================
11, 7公倍數
11 x 7 = 77, 77/17=4.......9
9 x 16 = 144 , 144/17=8 ....8
所以 7 x 11 x 16= 1232
=======================
1232 + 374 + 357 = 1963
1963 - N的公倍數
所以11x 7x 17= 1309(N的公倍數)
1963-1309=654
所以三位數是654
Ans:654
========================
不知我寫您看懂否?
sam
訪客 (未驗證)
Re: 求救!!
2005-10-11 00:01is990101
Re: 求救!!
2005-11-28 15:37孫文先
Re: 求救!!
2005-12-01 09:56qqwwee2006
Re: 求救!!
2006-02-19 23:06