大數分解因數
2007-02-08 4:18 am
請回答 600600，900900，999999 的所有因數。( 據我所知，單是 600600的因數就有1，2，3，4，5，6，7，8，10，11，12，13，14，15，20...........................)
回答 (2)
2007-02-08 9:22 am
✔ 最佳答案
計法是:先求質因式
再將質因式的每個子數加1, 然後相乘, 求積
600600
質因式是: 2^3 x 3 x 5^2 x 7 x 11 x 13
所有子數加1的積: (3+1) x (1+1) x (2+1) x (1+1) x (1+1) x (1+1)
=4 x 2 x 3 x 2 x 2 x 2
=192
即 600600 共有 192 個因數(包括 1 和 600600)
900900
2^2 x 3^2 x 5^2 x 7 x 11 x 13
= 3 x 3 x 3 x 2 x 2 x 2
=216
999999
3^3 x 7 x 11 x 13 x 37 ***
= 4 x 2 x 2x 2 x 2
=64
參考: Yahoo Knowledge
2007-02-08 4:47 am
600600=1x600600
=2x300300
=3x200200
=4x150150
=5x120120
=6x100100
=7x85800
=8x75075
=10x60060
=11x54600
=12x50050
=13x46200
=14x42900
=15x40040
=20x30030
=21x28600
=22x27300
=24x25025
=25x24024
=26x23100
=28x21450
=30x20020
=33x18200
=35x17160
=39x15400
=40x15015
=42x14300
=44x13650
=50x12012
=52x11550
=55x10920
=56x10725
=60x10010
=65x9240
=66x9100
=70x8580
=75x8008
=77x7800
=78x7700
=84x7150
=88x6825
=91x6600
=100x6006
.
.
.
=770x780
=2x300300
=3x200200
=4x150150
=5x120120
=6x100100
=7x85800
=8x75075
=10x60060
=11x54600
=12x50050
=13x46200
=14x42900
=15x40040
=20x30030
=21x28600
=22x27300
=24x25025
=25x24024
=26x23100
=28x21450
=30x20020
=33x18200
=35x17160
=39x15400
=40x15015
=42x14300
=44x13650
=50x12012
=52x11550
=55x10920
=56x10725
=60x10010
=65x9240
=66x9100
=70x8580
=75x8008
=77x7800
=78x7700
=84x7150
=88x6825
=91x6600
=100x6006
.
.
.
=770x780
收錄日期: 2021-04-12 23:24:52
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070207000051KK03433