479,001,600
479,001,600 is 12 factorial — the number of ways to arrange twelve distinct objects.
- Even
- Composite
Where 479,001,600 fits
Why 479,001,600 is special
Twelve is where factorials stop fitting in a signed 32-bit integer: 13! is 6,227,020,800, which overflows. That makes 12! a real boundary in older software rather than only a mathematical value, and it is why permutation code so often caps at twelve.
479,001,600 is part of
Factors & digit properties
- Divisors (792)
- 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 27, 28, 30, 32, 33, 35, 36, 40, 42, 44, 45, 48, 50, 54, 55, 56, 60, 63, 64, 66, 70, 72, 75, 77, 80, 81, 84, 88, 90, 96, 99, 100, 105, 108, 110, 112, 120, 126, 128, 132, 135, 140, 144, 150, 154, 160, 162, 165, 168, 175, 176, 180, 189, 192, 198, 200, 210, 216, 220, 224, 225, 231, 240, 243, 252, 256, 264, 270, 275, 280, 288, 297, 300, 308, 315, 320, 324, 330, 336, 350, 352, 360, 378, 384, 385, 396, 400, 405, 420, 432, 440, 448, 450, 462, 480, 486, 495, 504, 512, 525, 528, 540, 550, 560, 567, 576, 594, 600, 616, 630, 640, 648, 660, 672, 675, 693, 700, 704, 720, 756, 768, 770, 792, 800, 810, 825, 840, 864, 880, 891, 896, 900, 924, 945, 960, 972, 990, 1008, 1024, 1050, 1056, 1080, 1100, 1120, 1134, 1152, 1155, 1188, 1200, 1215, 1232, 1260, 1280, 1296, 1320, 1344, 1350, 1386, 1400, 1408, 1440, 1485, 1512, 1536, 1540, 1575, 1584, 1600, 1620, 1650, 1680, 1701, 1728, 1760, 1782, 1792, 1800, 1848, 1890, 1920, 1925, 1944, 1980, 2016, 2025, 2079, 2100, 2112, 2160, 2200, 2240, 2268, 2304, 2310, 2376, 2400, 2430, 2464, 2475, 2520, 2560, 2592, 2640, 2673, 2688, 2700, 2772, 2800, 2816, 2835, 2880, 2970, 3024, 3072, 3080, 3150, 3168, 3200, 3240, 3300, 3360, 3402, 3456, 3465, 3520, 3564, 3584, 3600, 3696, 3780, 3840, 3850, 3888, 3960, 4032, 4050, 4158, 4200, 4224, 4320, 4400, 4455, 4480, 4536, 4608, 4620, 4725, 4752, 4800, 4860, 4928, 4950, 5040, 5120, 5184, 5280, 5346, 5376, 5400, 5544, 5600, 5632, 5670, 5760, 5775, 5940, 6048, 6075, 6160, 6237, 6300, 6336, 6400, 6480, 6600, 6720, 6804, 6912, 6930, 7040, 7128, 7168, 7200, 7392, 7425, 7560, 7680, 7700, 7776, 7920, 8064, 8100, 8316, 8400, 8448, 8505, 8640, 8800, 8910, 8960, 9072, 9216, 9240, 9450, 9504, 9600, 9720, 9856, 9900, 10080, 10368, 10395, 10560, 10692, 10752, 10800, 11088, 11200, 11264, 11340, 11520, 11550, 11880, 12096, 12150, 12320, 12474, 12600, 12672, 12800, 12960, 13200, 13365, 13440, 13608, 13824, 13860, 14080, 14175, 14256, 14400, 14784, 14850, 15120, 15360, 15400, 15552, 15840, 16128, 16200, 16632, 16800, 16896, 17010, 17280, 17325, 17600, 17820, 17920, 18144, 18480, 18711, 18900, 19008, 19200, 19440, 19712, 19800, 20160, 20736, 20790, 21120, 21384, 21504, 21600, 22176, 22275, 22400, 22680, 23040, 23100, 23760, 24192, 24300, 24640, 24948, 25200, 25344, 25600, 25920, 26400, 26730, 26880, 27216, 27648, 27720, 28160, 28350, 28512, 28800, 29568, 29700, 30240, 30800, 31104, 31185, 31680, 32256, 32400, 33264, 33600, 33792, 34020, 34560, 34650, 35200, 35640, 35840, 36288, 36960, 37422, 37800, 38016, 38400, 38880, 39424, 39600, 40320, 41472, 41580, 42240, 42525, 42768, 43200, 44352, 44550, 44800, 45360, 46080, 46200, 47520, 48384, 48600, 49280, 49896, 50400, 50688, 51840, 51975, 52800, 53460, 53760, 54432, 55440, 56320, 56700, 57024, 57600, 59136, 59400, 60480, 61600, 62208, 62370, 63360, 64512, 64800, 66528, 66825, 67200, 68040, 69120, 69300, 70400, 71280, 72576, 73920, 74844, 75600, 76032, 76800, 77760, 78848, 79200, 80640, 82944, 83160, 84480, 85050, 85536, 86400, 88704, 89100, 89600, 90720, 92400, 93555, 95040, 96768, 97200, 98560, 99792, 100800, 101376, 103680, 103950, 105600, 106920, 107520, 108864, 110880, 113400, 114048, 115200, 118272, 118800, 120960, 123200, 124416, 124740, 126720, 129600, 133056, 133650, 134400, 136080, 138240, 138600, 140800, 142560, 145152, 147840, 149688, 151200, 152064, 155520, 155925, 158400, 161280, 166320, 168960, 170100, 171072, 172800, 177408, 178200, 179200, 181440, 184800, 187110, 190080, 193536, 194400, 197120, 199584, 201600, 207360, 207900, 211200, 213840, 217728, 221760, 226800, 228096, 230400, 236544, 237600, 241920, 246400, 248832, 249480, 253440, 259200, 266112, 267300, 268800, 272160, 277200, 281600, 285120, 290304, 295680, 299376, 302400, 304128, 311040, 311850, 316800, 322560, 332640, 340200, 342144, 345600, 354816, 356400, 362880, 369600, 374220, 380160, 388800, 394240, 399168, 403200, 414720, 415800, 422400, 427680, 435456, 443520, 453600, 456192, 467775, 475200, 483840, 492800, 498960, 506880, 518400, 532224, 534600, 537600, 544320, 554400, 570240, 580608, 591360, 598752, 604800, 622080, 623700, 633600, 665280, 680400, 684288, 691200, 709632, 712800, 725760, 739200, 748440, 760320, 777600, 798336, 806400, 831600, 844800, 855360, 870912, 887040, 907200, 912384, 935550, 950400, 967680, 985600, 997920, 1036800, 1064448, 1069200, 1088640, 1108800, 1140480, 1182720, 1197504, 1209600, 1244160, 1247400, 1267200, 1330560, 1360800, 1368576, 1425600, 1451520, 1478400, 1496880, 1520640, 1555200, 1596672, 1612800, 1663200, 1710720, 1741824, 1774080, 1814400, 1871100, 1900800, 1971200, 1995840, 2073600, 2128896, 2138400, 2177280, 2217600, 2280960, 2395008, 2419200, 2494800, 2534400, 2661120, 2721600, 2737152, 2851200, 2903040, 2956800, 2993760, 3110400, 3193344, 3326400, 3421440, 3548160, 3628800, 3742200, 3801600, 3991680, 4276800, 4354560, 4435200, 4561920, 4790016, 4838400, 4989600, 5322240, 5443200, 5702400, 5913600, 5987520, 6220800, 6386688, 6652800, 6842880, 7257600, 7484400, 7603200, 7983360, 8553600, 8709120, 8870400, 9580032, 9979200, 10644480, 10886400, 11404800, 11975040, 13305600, 13685760, 14515200, 14968800, 15966720, 17107200, 17740800, 19160064, 19958400, 21772800, 22809600, 23950080, 26611200, 29937600, 31933440, 34214400, 39916800, 43545600, 47900160, 53222400, 59875200, 68428800, 79833600, 95800320, 119750400, 159667200, 239500800, 479001600
- Prime factorisation
- 2^10 × 3^5 × 5^2 × 7 × 11
- Digit sum
- 27
- Digital root
- 9
Representations
- Decimal
- 479001600
- Scientific notation
- 4.790 × 10^8
Roman numerals
Roman numerals as modelled here goes up to 3,999.
Binary
1 1 1 0 0 1 0 0 0 1 1 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0
1 × 268,435,456 + 1 × 134,217,728 + 1 × 67,108,864 + 0 × 33,554,432 + 0 × 16,777,216 + 1 × 8,388,608 + 0 × 4,194,304 + 0 × 2,097,152 + 0 × 1,048,576 + 1 × 524,288 + 1 × 262,144 + 0 × 131,072 + 0 × 65,536 + 1 × 32,768 + 1 × 16,384 + 1 × 8,192 + 1 × 4,096 + 1 × 2,048 + 1 × 1,024 + 0 × 512 + 0 × 256 + 0 × 128 + 0 × 64 + 0 × 32 + 0 × 16 + 0 × 8 + 0 × 4 + 0 × 2 + 0 × 1 = 479,001,600
Octal
3 4 4 3 1 7 6 0 0 0
3 × 134,217,728 + 4 × 16,777,216 + 4 × 2,097,152 + 3 × 262,144 + 1 × 32,768 + 7 × 4,096 + 6 × 512 + 0 × 64 + 0 × 8 + 0 × 1 = 479,001,600
Hexadecimal
1 c 8 c f c 0 0
1 × 268,435,456 + c × 16,777,216 + 8 × 1,048,576 + c × 65,536 + f × 4,096 + c × 256 + 0 × 16 + 0 × 1 = 479,001,600
Other mathematical patterns
- Abundant number
- Factorial number
- Harshad (Niven) number
Related numbers & connections
479001600 appears in Numbers in measurement, the topic covering numbers that carry a documented measurement fact.
Numbers Around Us
- appears inUnits and measurement
why?
Strength 0.50, confidence "high".
Science
The number of ways to arrange twelve distinct objects is 479,001,600 (worldwide, combinatorics). Twelve factorial, and the last factorial that fits in a signed 32-bit integer — 13! overflows, which is why permutation code so often stops at twelve.
DocumentedScienceGeography: worldwide, combinatorics
Common questions
Is 479,001,600 a prime number?
No, 479,001,600 is not prime.
What are the factors of 479,001,600?
The factors of 479,001,600 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 27, 28, 30, 32, 33, 35, 36, 40, 42, 44, 45, 48, 50, 54, 55, 56, 60, 63, 64, 66, 70, 72, 75, 77, 80, 81, 84, 88, 90, 96, 99, 100, 105, 108, 110, 112, 120, 126, 128, 132, 135, 140, 144, 150, 154, 160, 162, 165, 168, 175, 176, 180, 189, 192, 198, 200, 210, 216, 220, 224, 225, 231, 240, 243, 252, 256, 264, 270, 275, 280, 288, 297, 300, 308, 315, 320, 324, 330, 336, 350, 352, 360, 378, 384, 385, 396, 400, 405, 420, 432, 440, 448, 450, 462, 480, 486, 495, 504, 512, 525, 528, 540, 550, 560, 567, 576, 594, 600, 616, 630, 640, 648, 660, 672, 675, 693, 700, 704, 720, 756, 768, 770, 792, 800, 810, 825, 840, 864, 880, 891, 896, 900, 924, 945, 960, 972, 990, 1008, 1024, 1050, 1056, 1080, 1100, 1120, 1134, 1152, 1155, 1188, 1200, 1215, 1232, 1260, 1280, 1296, 1320, 1344, 1350, 1386, 1400, 1408, 1440, 1485, 1512, 1536, 1540, 1575, 1584, 1600, 1620, 1650, 1680, 1701, 1728, 1760, 1782, 1792, 1800, 1848, 1890, 1920, 1925, 1944, 1980, 2016, 2025, 2079, 2100, 2112, 2160, 2200, 2240, 2268, 2304, 2310, 2376, 2400, 2430, 2464, 2475, 2520, 2560, 2592, 2640, 2673, 2688, 2700, 2772, 2800, 2816, 2835, 2880, 2970, 3024, 3072, 3080, 3150, 3168, 3200, 3240, 3300, 3360, 3402, 3456, 3465, 3520, 3564, 3584, 3600, 3696, 3780, 3840, 3850, 3888, 3960, 4032, 4050, 4158, 4200, 4224, 4320, 4400, 4455, 4480, 4536, 4608, 4620, 4725, 4752, 4800, 4860, 4928, 4950, 5040, 5120, 5184, 5280, 5346, 5376, 5400, 5544, 5600, 5632, 5670, 5760, 5775, 5940, 6048, 6075, 6160, 6237, 6300, 6336, 6400, 6480, 6600, 6720, 6804, 6912, 6930, 7040, 7128, 7168, 7200, 7392, 7425, 7560, 7680, 7700, 7776, 7920, 8064, 8100, 8316, 8400, 8448, 8505, 8640, 8800, 8910, 8960, 9072, 9216, 9240, 9450, 9504, 9600, 9720, 9856, 9900, 10080, 10368, 10395, 10560, 10692, 10752, 10800, 11088, 11200, 11264, 11340, 11520, 11550, 11880, 12096, 12150, 12320, 12474, 12600, 12672, 12800, 12960, 13200, 13365, 13440, 13608, 13824, 13860, 14080, 14175, 14256, 14400, 14784, 14850, 15120, 15360, 15400, 15552, 15840, 16128, 16200, 16632, 16800, 16896, 17010, 17280, 17325, 17600, 17820, 17920, 18144, 18480, 18711, 18900, 19008, 19200, 19440, 19712, 19800, 20160, 20736, 20790, 21120, 21384, 21504, 21600, 22176, 22275, 22400, 22680, 23040, 23100, 23760, 24192, 24300, 24640, 24948, 25200, 25344, 25600, 25920, 26400, 26730, 26880, 27216, 27648, 27720, 28160, 28350, 28512, 28800, 29568, 29700, 30240, 30800, 31104, 31185, 31680, 32256, 32400, 33264, 33600, 33792, 34020, 34560, 34650, 35200, 35640, 35840, 36288, 36960, 37422, 37800, 38016, 38400, 38880, 39424, 39600, 40320, 41472, 41580, 42240, 42525, 42768, 43200, 44352, 44550, 44800, 45360, 46080, 46200, 47520, 48384, 48600, 49280, 49896, 50400, 50688, 51840, 51975, 52800, 53460, 53760, 54432, 55440, 56320, 56700, 57024, 57600, 59136, 59400, 60480, 61600, 62208, 62370, 63360, 64512, 64800, 66528, 66825, 67200, 68040, 69120, 69300, 70400, 71280, 72576, 73920, 74844, 75600, 76032, 76800, 77760, 78848, 79200, 80640, 82944, 83160, 84480, 85050, 85536, 86400, 88704, 89100, 89600, 90720, 92400, 93555, 95040, 96768, 97200, 98560, 99792, 100800, 101376, 103680, 103950, 105600, 106920, 107520, 108864, 110880, 113400, 114048, 115200, 118272, 118800, 120960, 123200, 124416, 124740, 126720, 129600, 133056, 133650, 134400, 136080, 138240, 138600, 140800, 142560, 145152, 147840, 149688, 151200, 152064, 155520, 155925, 158400, 161280, 166320, 168960, 170100, 171072, 172800, 177408, 178200, 179200, 181440, 184800, 187110, 190080, 193536, 194400, 197120, 199584, 201600, 207360, 207900, 211200, 213840, 217728, 221760, 226800, 228096, 230400, 236544, 237600, 241920, 246400, 248832, 249480, 253440, 259200, 266112, 267300, 268800, 272160, 277200, 281600, 285120, 290304, 295680, 299376, 302400, 304128, 311040, 311850, 316800, 322560, 332640, 340200, 342144, 345600, 354816, 356400, 362880, 369600, 374220, 380160, 388800, 394240, 399168, 403200, 414720, 415800, 422400, 427680, 435456, 443520, 453600, 456192, 467775, 475200, 483840, 492800, 498960, 506880, 518400, 532224, 534600, 537600, 544320, 554400, 570240, 580608, 591360, 598752, 604800, 622080, 623700, 633600, 665280, 680400, 684288, 691200, 709632, 712800, 725760, 739200, 748440, 760320, 777600, 798336, 806400, 831600, 844800, 855360, 870912, 887040, 907200, 912384, 935550, 950400, 967680, 985600, 997920, 1036800, 1064448, 1069200, 1088640, 1108800, 1140480, 1182720, 1197504, 1209600, 1244160, 1247400, 1267200, 1330560, 1360800, 1368576, 1425600, 1451520, 1478400, 1496880, 1520640, 1555200, 1596672, 1612800, 1663200, 1710720, 1741824, 1774080, 1814400, 1871100, 1900800, 1971200, 1995840, 2073600, 2128896, 2138400, 2177280, 2217600, 2280960, 2395008, 2419200, 2494800, 2534400, 2661120, 2721600, 2737152, 2851200, 2903040, 2956800, 2993760, 3110400, 3193344, 3326400, 3421440, 3548160, 3628800, 3742200, 3801600, 3991680, 4276800, 4354560, 4435200, 4561920, 4790016, 4838400, 4989600, 5322240, 5443200, 5702400, 5913600, 5987520, 6220800, 6386688, 6652800, 6842880, 7257600, 7484400, 7603200, 7983360, 8553600, 8709120, 8870400, 9580032, 9979200, 10644480, 10886400, 11404800, 11975040, 13305600, 13685760, 14515200, 14968800, 15966720, 17107200, 17740800, 19160064, 19958400, 21772800, 22809600, 23950080, 26611200, 29937600, 31933440, 34214400, 39916800, 43545600, 47900160, 53222400, 59875200, 68428800, 79833600, 95800320, 119750400, 159667200, 239500800, 479001600.
About this page's data
Mathematical facts:computed directly from the number's value — nothing to source or verify externally.
Contextual records: 1 reviewer-confirmed record, sourced and reviewed before publication.
Last reviewed: 15 July 2026