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# is there a easier way to do this other than using long multiplication

+1
173
2
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Find the product of the positive divisors of 9!.

Jun 14, 2021

#1
+2312
+1

I can't think of a fast method, but you could find the number of factors, divide that by 2 and multiply 9! by it?

=^._.^=

Jun 15, 2021
#2
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(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 27, 28, 30, 32, 35, 36, 40, 42, 45, 48, 54, 56, 60, 63, 64, 70, 72, 80, 81, 84, 90, 96, 105, 108, 112, 120, 126, 128, 135, 140, 144, 160, 162, 168, 180, 189, 192, 210, 216, 224, 240, 252, 270, 280, 288, 315, 320, 324, 336, 360, 378, 384, 405, 420, 432, 448, 480, 504, 540, 560, 567, 576, 630, 640, 648, 672, 720, 756, 810, 840, 864, 896, 945, 960, 1008, 1080, 1120, 1134, 1152, 1260, 1296, 1344, 1440, 1512, 1620, 1680, 1728, 1890, 1920, 2016, 2160, 2240, 2268, 2520, 2592, 2688, 2835, 2880, 3024, 3240, 3360, 3456, 3780, 4032, 4320, 4480, 4536, 5040, 5184, 5670, 5760, 6048, 6480, 6720, 7560, 8064, 8640, 9072, 10080, 10368, 11340, 12096, 12960, 13440, 15120, 17280, 18144, 20160, 22680, 24192, 25920, 30240, 36288, 40320, 45360, 51840, 60480, 72576, 90720, 120960, 181440, 362880)>>Total Number ==160 divisors>>Their Product==6.040079156 x 10^444

Jun 15, 2021