Numbers 980,000,000s

A page of the Numeropedia - the Special Encyclopedia of Numbers

900,000,000 –  910,000,000920,000,000930,000,000 – 940,000,000

[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 ...

982,451,653

[Math.]  The 50,000,000th prime number.

984,390,625

[Math.]  Sum of the first 250 cube numbers:

13+23+…+2503 = 984,390,625 = (1+2+…+250)2 = 31,3752.

987,653,214

[Math.] A Smith number, using all 9 digits 1-9 once.

987,654,103

[Math.]  The largest prime number of 9 different digits.

987,654,312

[Math.]  Numbers 123,456,789 and its multiples:

123,456,789×2 = 246,913,578, 123,456,789×4 = 493,827,156,

123,456,789×5 = 617,283,945, 123,456,789×7 = 864,197,523 and

123,456,789×8 = 987,654,312 are all zero-less pan-digital numbers.

Hence, there are zero-less pan-digital number equalities:

123,456,789´493,827,156 = 246,913,5782

246,913,578´987,654,312 = 493,827,1562.

Also, multiples of 123,456,789 with some numbers from 10 to 80, give pan-digital numbers.

987,654,320

[Math.] Multiples of 012345679 by 8, 17, 26, 35, 44, 53, 62, 71 and 80 will yield all 9 rotations of the number 098765432: 098765432, 209876543, 320987654, 432098765, 543209876, 654320987, 765432098, 876543209 and 987654320. All numbers are missing digit 1.

987,654,321

[Math.] The largest number of 9 different digits.

[Math.] 123,456,789×989,010,989 = 122,100,120,987,654,321.

[Math.] 987,654,321–123,456,789 = 864,197,532; All 3 numbers are zero-less pan-digital.

[Math.]  The numbers 987654321,

987654321×2 = 1975308642,

987654321×4 = 3950617284,

987654321×5 = 4938271605,

987654321×7 = 6913580247,

987654321×8 = 7901234568 and

987654321×10 = 9,876,543,210 are all pan-digital numbers.

[Math.]

987,654,321×09 = 08,888,888,889

987,654,321×18 = 17,777,777,778

987,654,321×27 = 26,666,666,667

987,654,321×36 = 35,555,555,556

987,654,321×45 = 44,444,444,445

987,654,321×54 = 53,333,333,334

987,654,321×63 = 62,222,222,223

987,654,321×72 = 71,111,111,112

987,654,321×81 = 80,000,000,001.

[Math.]

9×9+(9–2) = 88

98×9+(9–3) = 888

987×9+(9–4) = 8,888

9,876×9+(9–5) = 88,888

98,765×9+(9–6) = 888,888

987,654×9+(9–7) = 8,888,888

9,876,543×9+(9–8) = 88,888,888

98,765,432×9+(9–9) = 888,888,888

987,654,321×9+(9–10) = 8,888,888,888

9,876,543,210×9+(9–11) = 88,888,888,888

98,765,432,099×9+(9–12) = 888,888,888,888  = 98,765,432,100×9–12.

987,654,320,988×9+(9–13) = 8,888,888,888,888

9,876,543,209,877×9+(9–14) = 88,888,888,888,888

...

[Math.]

1×8+1 = 9

12×8+2 = 98

123×8+3 = 987

1,234×8+4 = 9,876

12,345×8+5 = 98,765

123,456×8+6 = 987,654

1,234,567×8+7 = 9,876,543

12,345,678×8+8 = 98,765,432

123,456,789×8+9 = 987,654,321

1,234,567,890×8+90 = 9,876,543,210

(start of a new cycle)

12,345,678,901×8+901 = 98,765,432,109

123,456,789,012×8+9,002 = 987,654,321,098

1,234,567,890,123×8+90,003 = 9,876,543,210,987

12,345,678,901,234×8+900,004 = 98,765,432,109,876

123,456,789,012,345×8+9,000,005 = 987,654,321,098,765

1,234,567,890,123,456×8+90,000,006 = 9,876,543,210,987,654

12,345,678,901,234,567×8+900,000,007 = 98,765,432,109,876,543

123,456,789,012,345,678×8+9,000,000,008 = 987,654,321,098,765,432

1,234,567,890,123,456,789×8+90000000009 = 9,876,543,210,987,654,321

12,345,678,901,234,567,890×8+ 900000000090 = 98,765,432,109,876,543,210

... (end of cycle) ...

989,999,901

[Math.]

(*)   332×9 = 1089×9 = 9,801 = 992 & 1089×9801 = 10,673,289 = 32672

1089…1089×9 = 9801…9801  & 1089…1089×9801…9801  = 3267…32672

(**)  10989×9 = 98901 & 10989×98901 = 1,086,823,089 = 329672

10989…10989×9 = 98901…98901 & 10989…10989×98901...98901 = 32967…329672

(***)   109999989×9 = 989999901 & 109999989×989999901 = 3299999672

109999989…109999989×9 = 989999901…989999901 &

109999989…109999989×989999901...989999901 = 32999967…3299999672

(****)  109…989×9 = 989…901 & 109...989×989…901 = 329…9672

109…989...109…989×9 = 989…901...989…901  &

109…989…109…989×989…901...989…901 = 329…967…329…9672.

989,010,989

[Math.]   989,010,989×123,456,789 = 122,100,120,987,654,321.

(989,010,989 is a palindromic number).

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.