# 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)

${252^2} + {275^2} = {373^2}$

$63,504 + 75,625 = 139,129$

$139,129 = 139,129$

You may also be interested in these related math lessons or tutorials:

What is a Pythagorean Triple?

Pythagorean Theorem

Pythagorean Theorem Practice Problems with Answers

Generating Pythagorean Triples