List of Pythagorean Triples

Below is a list of Pythagorean Triples. The triples in this list are by no means exhaustive in nature because there are infinite numbers of Pythagorean Triples.

The Pythagorean Triples here are also called Primitive Pythagorean Triples because the Greatest Common Divisor (GCD) or the Greatest Common Factor (GCF) of the three positive integers is equal to 1.

Suppose we have a set of three (3) positive integers,

\left( {a,b,c} \right)

they are Pythagorean Triples if it satisfies the equation,

{a^2} + {b^2} = {c^2}

where the GCD of a,b,c equals 1.

It also implies that a,b and c are relatively prime numbers which simply means that their Greatest Common Factor is 1.


List of Primitive Pythagorean Triples

(3, 4, 5)

{3^2} + {4^2} = {5^2}9 + 16 = 2525 = 25

(5, 12, 13)

{5^2} + {12^2} = {13^2}25 + 144 = 169169 = 169

(7, 24, 25)

{7^2} + {24^2} = {25^2}49 + 576 = 625625 = 625

(8, 15, 17)

{8^2} + {15^2} = {17^2}64+225=289289=289

(9, 40, 41)

{9^2} + {40^2} = {41^2}81 + 1,600 = 1,6811,681 = 1,681

(11, 60, 61)

{11^2} + {60^2} = {61^2}121 + 3,600 = 3,7213,721 = 3,721

(12, 35, 37)

{12^2} + {35^2} = {37^2}144 + 1,225 = 1,3691,369 = 1,369

(13, 84, 85)

{13^2} + {84^2} = {85^2}169 + 7,056 = 7,2257,225 = 7,225

(15, 112, 113)

{15^2} + {112^2} = {113^2}225 + 12,544 = 12,76912,769 = 12,769

(16, 63, 65)

{16^2} + {63^2} = {65^2}256 + 3,969 = 4,2254,225 = 4,225

(17, 144, 145)

{17^2} + {144^2} = {145^2}289 + 20,736 = 21,02521,025 = 21,025

(19, 180, 181)

{19^2} + {180^2} = {181^2}361 + 32,400 = 32,76132,761 = 32,761

(20, 21, 29)

{20^2} + {21^2} = {29^2}400 + 441 = 841841 = 841

(20, 99, 101)

{20^2} + {99^2} = {101^2}400 + 9,801 = 10,20110,201 = 10,201

(21, 220, 221)

{21^2} + {220^2} = {221^2}441 + 48,400 = 48,84148,841 = 48,841

(23, 264, 265)

{23^2} + {264^2} = {265^2}529 + 69,696 = 70,22570,225 = 70,225

(24, 143, 145)

{24^2} + {143^2} = {145^2}576 + 20,449 = 21,02521,025 = 21,025

(25, 312, 313)

{25^2} + {312^2} = {313^2}625 + 97,344 = 97,96997,969 = 97,969

(27, 364, 365)

{27^2} + {364^2} = {365^2}729 + 132,496 = 133,225133,225 = 133,225

(28, 45, 53)

{28^2} + {45^2} = {53^2}784 + 2,025 = 2,8902,890 = 2,890

(28, 195, 197)

{28^2} + {195^2} = {197^2}784 + 38,025 = 38,80938,809 = 38,809

(29, 420, 421)

{29^2} + {420^2} = {421^2}841 + 176,400 = 177,241177,241 = 177,241

(31, 480, 481)

{31^2} + {480^2} = {481^2}961 + 230,400 = 231,361231,361 = 231,361

(32, 255, 257)

{32^2} + {255^2} = {257^2}1,024 + 65,025 = 66,04966,049 = 66,049

(33, 56, 65)

{33^2} + {56^2} = {65^2}1,089 + 3,136 = 4,2254,225 = 4,225

(33, 544, 545)

{33^2} + {544^2} = {545^2}1,089 + 295,936 = 297,025297,025 = 297,025

(35, 612, 613)

{35^2} + {612^2} = {613^2}1,225 + 374,544 = 375,769375,769 = 375,769

(36, 77, 85)

{36^2} + {77^2} = {88^2}1,296 + 5,929 = 7,2257,225 = 7,225

(36, 323, 325)

{36^2} + {323^2} = {325^2}1,296 + 104,439 = 105,625105,625 = 105,625

(37, 684, 685)

{37^2} + {684^2} = {685^2}1,369 + 467,856 = 469,225469,225 = 469,225

(39, 80, 89)

{39^2} + {80^2} = {89^2}1,521 + 6,400 = 7,9217,921 = 7,921

(39, 760, 761)

{39^2} + {760^2} = {761^2}1,521 + 577,600 = 579,121579,121 = 579,121

(41, 840, 841)

{41^2} + {840^2} = {841^2}1,681 + 705,600 = 707,281707,281 = 707,281

(43, 924, 925)

{43^2} + {924^2} = {925^2}1,849 + 853,776 = 855,625855,625 = 855,625

(44, 117, 125)

{44^2} + {117^2} = {125^2}1,936 + 13,689 = 15,62515,625 = 15,625

(45, 1012, 1013)

{45^2} + {1,012^2} = {1,013^2}2,025 + 1,024,144 = 1,026,1691,026,169 = 1,026,169

(47, 1104, 1105)

{47^2} + {1,104^2} = {1,105^2}2,209 + 1,218,816 = 1,221,0251,221,025 = 1,221,025

(48, 55, 73)

{48^2} + {55^2} = {73^2}2,304 + 3,025 = 5,3295,329 = 5,329

(49, 1200, 1201)

{49^2} + {1,200^2} = {1,201^2}2,401 + 1,440,000 = 1,442,4011,442,401 = 1,442,401

(51, 140, 149)

{51^2} + {140^2} = {149^2}2,601 + 19,600 = 22,20122,201 = 22,201

(52, 165, 173)

{52^2} + {165^2} = {173^2}2,704 + 27,225 = 29,92929,929 = 29,929

(57, 176, 185)

{57^2} + {176^2} = {185^2}3,249 + 30,976 = 34,22534,225 = 34,225

(60, 91, 109)

{60^2} + {91^2} = {109^2}3,600 + 8,281 = 11,88111,881 = 11,881

(60, 221, 229)

{60^2} + {221^2} = {229^2}3,600 + 48,841 = 52,44152,441 = 52,441

(65, 72, 97)

{65^2} + {72^2} = {97^2}4,225 + 5,184 = 9,4099,409 = 9,409

(68, 285, 293)

{68^2} + {285^2} = {293^2}4,624 + 81,225 = 85,84985,849 = 85,849

(69, 260, 269)

{69^2} + {260^2} = {269^2}4,761 + 67,600 = 72,36172,361 = 72,361

(84, 187, 205)

{84^2} + {187^2} = {205^2}7,056 + 34,969 = 42,02542,025 = 42,025

(85, 132, 157)

{85^2} + {132^2} = {157^2}7,225 + 174,424 = 24,64924,649 = 24,649

(88, 105, 137)

{88^2} + {105^2} = {137^2}7,744 + 11,025 = 18,76918,769 = 18,769

(95, 168, 193)

{95^2} + {168^2} = {193^2}9,025 + 28,224 = 37,24937,249 = 37,249

(96, 247, 265)

{96^2} + {247^2} = {265^2}9,216 + 61,009 = 70,22570,225 = 70,225

(104, 153, 185)

{104^2} + {153^2} = {185^2}10,816 + 23,409 = 34,22534,225 = 34,225

(105, 208, 233)

{105^2} + {208^2} = {233^2}11,025 + 43,264 = 54,28954,289 = 54,289

(115, 252, 277)

{115^2} + {252^2} = {277^2}13,225 + 63,504 = 76,72976,729 = 76,729

(119, 120, 169)

{119^2} + {120^2} = {169^2}14,161 + 14,400 = 28,56128,561 = 28,561

(120, 209, 241)

{120^2} + {209^2} = {241^2}14,400 + 43,681 = 58,08158,081 = 58,081

(133, 156, 205)

{133^2} + {156^2} = {205^2}17,689 + 24,336 = 42,02542,025 = 42,025

(136, 273, 305)

{136^2} + {273^2} = {305^2}18,496 + 74,529 = 93,02593,025 = 93,025

(140, 171, 221)

{140^2} + {171^2} = {221^2}19,600 + 29,241 = 48,84148,841 = 48,841

(160, 231, 281)

{160^2} + {231^2} = {281^2}25,600 + 53,361 = 78,96178,961 = 78,961

(161, 240, 289)

{161^2} + {240^2} = {289^2}25,921 + 57,600 = 83,52183,521 = 83,521

(175, 288, 337)

{175^2} + {288^2} = {337^2}30,625 + 82,944 = 113,569113,569 = 113,569

(180, 299, 349)

{180^2} + {299^2} = {349^2}32,400 + 89,401 = 121,801121,801 = 121,801

(204, 253, 325)

{204^2} + {253^2} = {325^2}41,616 + 64,009 = 105,625105,625 = 105,625

(207, 224, 305)

{207^2} + {224^2} = {305^2}42,849 + 50,176 = 93,02593,025 = 93,025

(225, 272, 353)

{225^2} + {272^2} = {353^2}50,625 + 73,984 = 124,609124,609 = 124,609

(252, 275, 373)

{252^2} + {275^2} = {373^2}63,504 + 75,625 = 139,129139,129 = 139,129

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