Numbers 33,000,000s

A page of the Numeropedia - the Special Encyclopedia of Numbers

31,000,00032,000,00033,000,00034,000,000

35,000,00036,000,00037,000,00038,000,00039,000,000

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33,087,205

[Math.]  33,087,205 = 114+213+312+411+510+69+78+87+96+105+114+123+132+141.

33,087,206

[Math.]

33,087,206 = 015+114+213+312+411+510+69+78+87+96+105+114+123+132+141+150.

33,333,332

[Math.]  Square of numbers of similar pattern xxy, where y = x–1.

* 1102 = 012,100 & 012+100 = 112 = 110+2

* 3322 = 110,224 & 110+224 = 334 = 332+2.

Similarly, 3…322 = 1…102…24 & 1…10+2…24 = 3…34 = 3…32+2.

33,333,3322 = 1111111022222224 & 11,111,110+22,222,224 = 33,333,334 = 33,333,332+2.

* 4432 = 196,249 & 196+249 = 445 = 443+2

* 6652 = 442,225 & 442+225 = 667 = 665+2.

Similarly, 6…652 = 4…422…25 & 4…42+2…25 = 6…67 = 6…65+2.

* 7762 = 602,176 & 602+176 = 778 = 776+2.

33,333,333

[Math.]

33333333,66666667,00000000 = 33,333,3333+66,666,6673+000000003

33333333,66666667,00000001 = 33,333,3333+66,666,6673+000000013. (Generalizable)

[Math.]  166,666,665,000,000,033,333,333 = 16,666,6663+50,000,0003+33,333,3333.

1,000,000,000,000,166,666,665,000,000,033,333,333 =

= (1012)3+16,666,6663+50,000,0003+33,333,3333. (Generalizable)

[Math.]

33,333,333´33,333,334 = 1,111,111,122,222,222

33,333,333´33,333,335 = 1,111,111,155,555,555

33,333,333´33,333,336 = 1,111,111,188,888,888

33,333,333´33,333,337 = 1,111,111,222,222,221.

33,333,333, 33,333,334, 33,333,335, 33,333,336, 33,333,337, 33,333,347 & 33,333,357

[Math.]

 33×34 = 1122 33×35 = 1155 33×36 = 1188 33×37 = 1221 33×47 = 1551 33×57 = 1881

...

 33333333×33333334= 1111111122222222 33333333×33333337= 1111111222222221 33333333×33333335= 1111111155555555 33333333×33333347= 1111111555555551 33333333×33333336= 1111111188888888 33333333×33333357= 1111111888888881

… (generalizable pattern) …

33,333,333 & 33,336,667

[Math.]

3×37 = 111

33×3367 = 111,111

333×333,667 = 111,111,111

3333×33336667 = 111,111,111,111

33333×3333366667 = 111,111,111,111,111

333333×333333666667 = 111,111,111,111,111,111

3333333×33333336666667 = 111,111,111,111,111,111,111

33333333×3333333366666667 = 111,111,111,111,111,111,111,111

333333333×333333333666666667 = 111,111,111,111,111,111,111,111,111

...

33,333,334

[Math.]  3,333,333,466,666,668 = 66,666,6682–33,333,3342

= (33333334+66666668)×33333334.

[Math.]  333,333,340,000,000,066,666,667 = 333333343+000000003+666666673

333,333,340,001,000,066,666,667 = 333333343+000100003+666666673.

(Generalizable)

[Math.]  Repeatedly inserting numbers 15 in the middle of the square number 16 yields other squares 1156 = 342, 111556 = 3342, 11115556 = 33342, 1111155556 = 333342

33,333,335

[Math.]  Repeatedly inserting numbers 12 between the digits 1 and 2 in the square number 1225 = 352 yields other squares 112225 = 3352, 11122225 = 33352, 1111222225 = 333352

[Math.]

296×333,667 = 98,765,432

2,996×33,336,667 = 99,876,654,332

29,996×3,333,366,667 = 99,987,666,543,332

299,996×333,333,666,667 = 99,998,766,665,433,332

2,999,996×33,333,336,666,667 = 99,999,876,666,654,333,332

29,999,996×3,333,333,366,666,667 = 99,999,987,666,666,543,333,332

[Math.]

372 = 1369 = 1368+1

33672 = 11336689 = 11336688+1

333,6672 = 111,333,666,889 = 111,333,666,888+1

3333,66672 = 1111,3333,6666,8889 = 1111,3333,6666,8888+1

...

33,346,668

[Math.]  33,346,668 = 66682–33342 = (3334+6668)×3334.

33,385,282

[Math.]  The 36th Lucas number.

33,385,284

[Math.]  Sum of the first 107 cube numbers:

13+23+…+1063+1073 = 33,385,284 = (1+2+…+106+107)2 = 57782.

33,445,755

[Math.]  The 38th Keith number.

33,501,825

[Math.]  A pair of amicable numbers (33501825, 36136575).

33,550,336

[Math.]  A triangular number (sum of all integers from 1 to 8191):

33550336 = 1+2+…+8190+8191.

33,550,336

[Math.]  The 5th perfect number; i.e., a number equal to the sum of all of its proper divisors, including 1 (or also called aliquot divisors). The first perfect numbers are: 6, 28, 496, 8128, 212(213–1) = 33550336, 216(217–1) = 8,589,869,056…

33,554,432 & 33,554,433

[Math.]  225 = 33,554,432 = 33,554,433 – 1.

33,669,999

[Math.]

692 = 136,161

36992 = 13682601

369992 = 1368926001

3699992 = 136899260001

36999992 = 13689992600001

369999992 = 1368999926000001

3366992 = 113366,216601

336699992 = 11336688,32660001

33669999992 = 1133668899,3266000001

3366999999992 = 113366889999,326600000001

333,666,9992 = 111,333,666,221,666,001

333,666,999,9992 = 111,333,666,888,332,666,000,001

333,666,999,999,9992 = 111,333,666,888,999,332,666,000,000,001

3333,6666,99992 = 1111,3333,6666,2221,6666,0001

3333,6666,9999,99992 = 1111,3333,6666,8888,3332,6666,0000,0001.

...

xy,abc,def

[Math.]  For any xy = 10 to 99, there are always six 6-digit numbers abc,edf such that the sum (xy+abc,def) is equal to one of 6 digit-rotations of 142,857 and the number xy,abc,def is a multiple of 142,857.

For any xy = 10 to 99, there are always twelve 6-digit numbers abc,edf such that the sum (xy+abc,def) is equal to one of 12 digit-rotations of 076,923 or 153,846 and the number xy,abc,def is a multiple of 76,923.