Numbers 240,000,000s

A page of the Numeropedia - the Special Encyclopedia of Numbers

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

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242,611,776

[Math.]  Sum of the first 176 cube numbers:

13+23+…+1763 = 242,611,776 = (1+2+…+176)2 = 15,5762.

244,140,625

[Math.]  The smallest 6th power that can be expressed as the sum of 6th powers:

244,140,625 = 256 = 16+26+36+56+66+76+86+96+106+126+136+156+166+176+186+236.

244,823,040

[Math.]  The order of the 9th sporadic group: Mathieu group M24.

245,893,761

[Math.]  156812 = 245,893,761, one of thirty 9-digit square numbers using all 9 digits 1-9 once.

246,913,578

[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.

246,913,580

[Math.]  Multiples of 012345679 by 2, 11, 20, 29, 38, 47, 56, 65 and 74 will yield all 9 rotations of 024691358: 024691358, 135802469, 246913580, 358024691, 469135802, 580246913, 691358024, 802469135 and 913580246. All numbers are missing digit 7.

248,157,009

[Math.]  Sum of the first 177 cube numbers:

13+23+…+1773 = 248,157,009 = (1+2+…+177)2 = 15,7532.

249,999,998

[Math.]  The number of 0’s that the factorial of 1 billion ends in.

249,999,998 = [[1,000,000,000/5]]+…+[[1,000,000,000/512]],

where [[x]] is the floor function of x, i.e. which is the largest integer less than x (or the integral part of x).

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.