Numbers 330,000,000s

A page of the Numeropedia - the Special Encyclopedia of Numbers

300,000,000 310,000,000320,000,000330,000,000 – 340,000,000

All Numbers  350,000,000360,000,000370,000,000380,000,000390,000,000

[1M] & [10M] & [100M- [200M] - [300M] - [400M] - [500M] - [600M] - [700M] - [800M] - [900M] & [1B]

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

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.

333,333,3322 = 111111110222222224 & 111111110+222222224 = 333,333,334 = 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. 

 

333,333,333

[Math.]  333333333,666666667,000000000 = 333,333,3333+666,666,6673+0000000003

and  333333333,666666667,000000001 = 333,333,3333+666,666,6673+0000000013.

 

166,666,666,500,000,000,333,333,333 = 

                  =  166,666,6663+500,000,0003+333,333,3333.   (Generalizable)

  

[Math.]  Number 12,345,679 multiplied by 9, 18, 27, 36, 45, 54, 63, 72 and 81 give 9 rep-digit numbers: 111111111, 222222222, 333333333,…, 999999999, respectively. 

 

[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

...

333,333,333, 333,333,334, 333,333,335, 333,333,33, 333,333,337,

333,333,347 & 333,333,357

[Math.]   

33×34 = 1122

33×35 = 1155

33×36 = 1188

33×37 = 1221

33×47 = 1551

33×57 = 1881

 ...

 

333333333×333333334=111111111222222222

333333333×333333337=111111112222222221

333333333×333333335=111111111555555555

333333333×333333347=111111115555555551

333333333×333333336=11111111888888888

333333333×333333357=111111118888888881

 … (generalizable pattern) …

 

333,333,334

[Math.]  333,333,334,666,666,668 = 666,666,6682–333,333,3342 =

= (333333334+666666668)×333333334.

 

333,333,334,000,000,000,666,666,667 =

= 333,333,3343+0000000003+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

 

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

 

333,666,999

[Math.]

692 = 136,161

36992 = 13682601

369992 = 1368926001

3699992 = 136899260001

36999992 = 13689992600001

369999992 = 1368999926000001

3699999992 = 136899999260000001

36999999992 = 1.3689999992600000001

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.

 ...

 

333,667,000

[Math.]  333,667,000 = 3333+6673+0003. (Generalizable)

 

333,667,001

[Math.] A prime number.  333,667,001 = 3333+6673+0013.  (Generalizable)

The smallest prime number has such property.

 

334,000,667

 [Math.]  334,000,667 = 3343+0003+6673. (Generalizable)

 

336,208,896

[Math.] Sum of the first 191 cube numbers:

13+23+…+1913 = 336,208,896 = (1+2+…+191)2 = 18,3362.

 

338,252,915

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

338,252,915 = 29262+…+29642 = 29652+…+30022.

 

xyz,abc,def

[Math.]  For any xyz = 100 to 999, there are always six 6-digit numbers abc,edf such that the sum (xyz+abc,def) is equal to one of 6 digit-rotations of 142,857 and the number  xyz,abc,def is a multiple of 142,857.

 

For any xyz = 100 to 999, there are always twelve 6-digit numbers abc,edf such that the sum (xyz+abc,def) is equal to one of 12 digit-rotations of 076,923 or 153,846 and the number xyz,abc,def is a multiple of 76,923.