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 = 25 25 = 25(5, 12, 13)
{5^2} + {12^2} = {13^2} 25 + 144 = 169 169 = 169(7, 24, 25)
{7^2} + {24^2} = {25^2} 49 + 576 = 625 625 = 625(8, 15, 17)
{8^2} + {15^2} = {17^2} 64+225=289 289=289(9, 40, 41)
{9^2} + {40^2} = {41^2} 81 + 1,600 = 1,681 1,681 = 1,681(11, 60, 61)
{11^2} + {60^2} = {61^2} 121 + 3,600 = 3,721 3,721 = 3,721(12, 35, 37)
{12^2} + {35^2} = {37^2} 144 + 1,225 = 1,369 1,369 = 1,369(13, 84, 85)
{13^2} + {84^2} = {85^2} 169 + 7,056 = 7,225 7,225 = 7,225(15, 112, 113)
{15^2} + {112^2} = {113^2} 225 + 12,544 = 12,769 12,769 = 12,769(16, 63, 65)
{16^2} + {63^2} = {65^2} 256 + 3,969 = 4,225 4,225 = 4,225(17, 144, 145)
{17^2} + {144^2} = {145^2} 289 + 20,736 = 21,025 21,025 = 21,025(19, 180, 181)
{19^2} + {180^2} = {181^2} 361 + 32,400 = 32,761 32,761 = 32,761(20, 21, 29)
{20^2} + {21^2} = {29^2} 400 + 441 = 841 841 = 841(20, 99, 101)
{20^2} + {99^2} = {101^2} 400 + 9,801 = 10,201 10,201 = 10,201(21, 220, 221)
{21^2} + {220^2} = {221^2} 441 + 48,400 = 48,841 48,841 = 48,841(23, 264, 265)
{23^2} + {264^2} = {265^2} 529 + 69,696 = 70,225 70,225 = 70,225(24, 143, 145)
{24^2} + {143^2} = {145^2} 576 + 20,449 = 21,025 21,025 = 21,025(25, 312, 313)
{25^2} + {312^2} = {313^2} 625 + 97,344 = 97,969 97,969 = 97,969(27, 364, 365)
{27^2} + {364^2} = {365^2} 729 + 132,496 = 133,225 133,225 = 133,225(28, 45, 53)
{28^2} + {45^2} = {53^2} 784 + 2,025 = 2,890 2,890 = 2,890(28, 195, 197)
{28^2} + {195^2} = {197^2} 784 + 38,025 = 38,809 38,809 = 38,809(29, 420, 421)
{29^2} + {420^2} = {421^2} 841 + 176,400 = 177,241 177,241 = 177,241(31, 480, 481)
{31^2} + {480^2} = {481^2} 961 + 230,400 = 231,361 231,361 = 231,361(32, 255, 257)
{32^2} + {255^2} = {257^2} 1,024 + 65,025 = 66,049 66,049 = 66,049(33, 56, 65)
{33^2} + {56^2} = {65^2} 1,089 + 3,136 = 4,225 4,225 = 4,225(33, 544, 545)
{33^2} + {544^2} = {545^2} 1,089 + 295,936 = 297,025 297,025 = 297,025(35, 612, 613)
{35^2} + {612^2} = {613^2} 1,225 + 374,544 = 375,769 375,769 = 375,769(36, 77, 85)
{36^2} + {77^2} = {85^2} 1,296 + 5,929 = 7,225 7,225 = 7,225(36, 323, 325)
{36^2} + {323^2} = {325^2} 1,296 + 104,439 = 105,625 105,625 = 105,625(37, 684, 685)
{37^2} + {684^2} = {685^2} 1,369 + 467,856 = 469,225 469,225 = 469,225(39, 80, 89)
{39^2} + {80^2} = {89^2} 1,521 + 6,400 = 7,921 7,921 = 7,921(39, 760, 761)
{39^2} + {760^2} = {761^2} 1,521 + 577,600 = 579,121 579,121 = 579,121(41, 840, 841)
{41^2} + {840^2} = {841^2} 1,681 + 705,600 = 707,281 707,281 = 707,281(43, 924, 925)
{43^2} + {924^2} = {925^2} 1,849 + 853,776 = 855,625 855,625 = 855,625(44, 117, 125)
{44^2} + {117^2} = {125^2} 1,936 + 13,689 = 15,625 15,625 = 15,625(45, 1012, 1013)
{45^2} + {1,012^2} = {1,013^2} 2,025 + 1,024,144 = 1,026,169 1,026,169 = 1,026,169(47, 1104, 1105)
{47^2} + {1,104^2} = {1,105^2} 2,209 + 1,218,816 = 1,221,025 1,221,025 = 1,221,025(48, 55, 73)
{48^2} + {55^2} = {73^2} 2,304 + 3,025 = 5,329 5,329 = 5,329(49, 1200, 1201)
{49^2} + {1,200^2} = {1,201^2} 2,401 + 1,440,000 = 1,442,401 1,442,401 = 1,442,401(51, 140, 149)
{51^2} + {140^2} = {149^2} 2,601 + 19,600 = 22,201 22,201 = 22,201(52, 165, 173)
{52^2} + {165^2} = {173^2} 2,704 + 27,225 = 29,929 29,929 = 29,929(57, 176, 185)
{57^2} + {176^2} = {185^2} 3,249 + 30,976 = 34,225 34,225 = 34,225(60, 91, 109)
{60^2} + {91^2} = {109^2} 3,600 + 8,281 = 11,881 11,881 = 11,881(60, 221, 229)
{60^2} + {221^2} = {229^2} 3,600 + 48,841 = 52,441 52,441 = 52,441(65, 72, 97)
{65^2} + {72^2} = {97^2} 4,225 + 5,184 = 9,409 9,409 = 9,409(68, 285, 293)
{68^2} + {285^2} = {293^2} 4,624 + 81,225 = 85,849 85,849 = 85,849(69, 260, 269)
{69^2} + {260^2} = {269^2} 4,761 + 67,600 = 72,361 72,361 = 72,361(84, 187, 205)
{84^2} + {187^2} = {205^2} 7,056 + 34,969 = 42,025 42,025 = 42,025(85, 132, 157)
{85^2} + {132^2} = {157^2} 7,225 + 174,424 = 24,649 24,649 = 24,649(88, 105, 137)
{88^2} + {105^2} = {137^2} 7,744 + 11,025 = 18,769 18,769 = 18,769(95, 168, 193)
{95^2} + {168^2} = {193^2} 9,025 + 28,224 = 37,249 37,249 = 37,249(96, 247, 265)
{96^2} + {247^2} = {265^2} 9,216 + 61,009 = 70,225 70,225 = 70,225(104, 153, 185)
{104^2} + {153^2} = {185^2} 10,816 + 23,409 = 34,225 34,225 = 34,225(105, 208, 233)
{105^2} + {208^2} = {233^2} 11,025 + 43,264 = 54,289 54,289 = 54,289(115, 252, 277)
{115^2} + {252^2} = {277^2} 13,225 + 63,504 = 76,729 76,729 = 76,729(119, 120, 169)
{119^2} + {120^2} = {169^2} 14,161 + 14,400 = 28,561 28,561 = 28,561(120, 209, 241)
{120^2} + {209^2} = {241^2} 14,400 + 43,681 = 58,081 58,081 = 58,081(133, 156, 205)
{133^2} + {156^2} = {205^2} 17,689 + 24,336 = 42,025 42,025 = 42,025(136, 273, 305)
{136^2} + {273^2} = {305^2} 18,496 + 74,529 = 93,025 93,025 = 93,025(140, 171, 221)
{140^2} + {171^2} = {221^2} 19,600 + 29,241 = 48,841 48,841 = 48,841(160, 231, 281)
{160^2} + {231^2} = {281^2} 25,600 + 53,361 = 78,961 78,961 = 78,961(161, 240, 289)
{161^2} + {240^2} = {289^2} 25,921 + 57,600 = 83,521 83,521 = 83,521(175, 288, 337)
{175^2} + {288^2} = {337^2} 30,625 + 82,944 = 113,569 113,569 = 113,569(180, 299, 349)
{180^2} + {299^2} = {349^2} 32,400 + 89,401 = 121,801 121,801 = 121,801(204, 253, 325)
{204^2} + {253^2} = {325^2} 41,616 + 64,009 = 105,625 105,625 = 105,625(207, 224, 305)
{207^2} + {224^2} = {305^2} 42,849 + 50,176 = 93,025 93,025 = 93,025(225, 272, 353)
{225^2} + {272^2} = {353^2} 50,625 + 73,984 = 124,609 124,609 = 124,609(252, 275, 373)
{252^2} + {275^2} = {373^2} 63,504 + 75,625 = 139,129 139,129 = 139,129Related lessons that might interest you: