# 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)

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

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