We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
132
1
avatar

How many moduli between 1 and 1,000 that have zero remainder does the number 25! have? Just to be clear:
25! mod 1, 2, 3, 4......1,000 =0. How many of them are there between 1 and 1,000? Thank you for help.

 Oct 22, 2018
 #1
avatar
0

I don't know if there is a shortcut or some formula to calculate this? Maybe somebody else on this forum does.

However, it is very easy to write a very short and simple computer code to check all the numbers from 1 up to 1,000. When you do that, this is what you get:

25! mod [1 to 1,000] =0 are the following numbers:

 

(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 60, 63, 64, 65, 66, 68, 69, 70, 72, 75, 76, 77, 78, 80, 81, 84, 85, 88, 90, 91, 92, 95, 96, 98, 99, 100, 102, 104, 105, 108, 110, 112, 114, 115, 117, 119, 120, 121, 125, 126, 128, 130, 132, 133, 135, 136, 138, 140, 143, 144, 147, 150, 152, 153, 154, 156, 160, 161, 162, 165, 168, 170, 171, 175, 176, 180, 182, 184, 187, 189, 190, 192, 195, 196, 198, 200, 204, 207, 208, 209, 210, 216, 220, 221, 224, 225, 228, 230, 231, 234, 238, 240, 242, 243, 245, 247, 250, 252, 253, 255, 256, 260, 264, 266, 270, 272, 273, 275, 276, 280, 285, 286, 288, 294, 297, 299, 300, 304, 306, 308, 312, 315, 320, 322, 323, 324, 325, 330, 336, 340, 342, 343, 345, 350, 351, 352, 357, 360, 363, 364, 368, 374, 375, 378, 380, 384, 385, 390, 391, 392, 396, 399, 400, 405, 408, 414, 416, 418, 420, 425, 429, 432, 437, 440, 441, 442, 448, 450, 455, 456, 459, 460, 462, 468, 475, 476, 480, 483, 484, 486, 490, 494, 495, 500, 504, 506, 510, 512, 513, 520, 525, 528, 532, 539, 540, 544, 546, 550, 552, 560, 561, 567, 570, 572, 575, 576, 585, 588, 594, 595, 598, 600, 605, 608, 612, 616, 621, 624, 625, 627, 630, 637, 640, 644, 646, 648, 650, 660, 663, 665, 672, 675, 680, 684, 686, 690, 693, 700, 702, 704, 714, 715, 720, 726, 728, 729, 735, 736, 741, 748, 750, 756, 759, 760, 765, 768, 770, 780, 782, 784, 792, 798, 800, 805, 810, 816, 819, 825, 828, 832, 833, 836, 840, 847, 850, 855, 858, 864, 874, 875, 880, 882, 884, 891, 896, 897, 900, 910, 912, 918, 920, 924, 931, 935, 936, 945, 950, 952, 960, 966, 968, 969, 972, 975, 980, 988, 990, 1000)
Total = 358

Man! That is a lot of numbers!!! If there isn't a formula, how are you supposed to calculate all of this?

 Oct 22, 2018

5 Online Users