Numbers 33,000,000,000s

A page of the Numeropedia - the Special Encyclopedia of Numbers

30,000,000,000 31,000,000,00032,000,000,000 – 33,000,000,00034,000,000,000

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

 All Numbers  – [1B] –  [10B] –  [20B] – [30B] – [40B] – [50B] – [60B] – [70B] – [80B] – [90B] & [100B]

1  - 10 - 100  - 1000 - 10,000 - 100,000 - 1M - 10M - 100M1B10B - 100B - 1T - 10T - 100T - 1Q ...

33,058,148,761

[Math.]   33,058,148,761 = (33,058+148,761)2 = 181,8192 and 669,420,148,761 = (669420+148761)2 = 818,1812 and 181819+818181 = 1,000,000.

 

33,162,595,236

[Math.]  Sum of the first 603 cube numbers:

13+…+6033 = 33,162,595,236 = (1+…+603)2 = 182,1062.

 

33,333,333,332

[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

33,333,333,3322 = 1111111111022222222224 & 11111111110+22222222224 =

33,333,333,334 = 33,333,333,332+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.

 

33,333,333,333 (separate page)

 

33,333,333,334

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

= (33333333334+66666666668)×33333333334.

333,333,333,340,000,000,000,066,666,666,667 =

= 33,333,333,3343+000000000003+66,666,666,6673. (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

 

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

[Math.]   

33×34 = 1122

33×35 = 1155

33×36 = 1188

33×37 = 1221

33×47 = 1551

33×57 = 1881

 ... (generalizable pattern) … 

 

33,333,333,333×33,333,333,334 = 1111111111122222222222

33,333,333,333×33,333,333,335 = 1111111111155555555555

33,333,333,333×33,333,333,336 = 1111111111188888888888

33,333,333,333×33,333,333,337 = 1111111111222222222221.

 

33,333,333,335

[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

 

33,337,333,333

[Math.]  33337333333 = 37×901,009,009.

 

33,382,944,100

[Math.]  Sum of the first 604 cube numbers:

13+…+6043 = 33,162,595,236 = (1+…+604)2 = 182,7102.

 

33,471,650,320

[Math.]  Two consecutive sums of consecutive square numbers:

33,471,650,320 = 185282+…+186242 = 186252+…+187202.

 

33,489,857,205

[Math.]  The number of 12-digit prime numbers (from 100,000,000,003 to 999,999,999,989).

 

33,604,389,225

[Math.]  Sum of the first 605 cube numbers:

13+…+6053 = 33,604,389,225 = (1+…+605)2 = 183,3152.

 

33,826,934,241

[Math.]  Sum of the first 606 cube numbers:

13+…+6063 = 33,826,934,241 = (1+…+606)2 = 183,9212.

 

xy,zwv,abc,def

[Math.]  For any xy,zwv = 10,000 to 99,999, there are always six 6-digit numbers abc,edf such that xy,zwv +abc,def is equal to one of 6 digit-rotations of 142,857 and the number xy,zwv,abc,def is a multiple of 142,857.

 

For any xy,zwv  = 10,000 to 76,922, there are always twelve 6-digit numbers abc,edf such that xy,zwv +abc,def is equal to one of 12 digit-rotations of 076,923 or 153,846 and the number xy,zwv,abc,def is a multiple of 76,923.