75 (number)

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← 74 75 76 →
Cardinalseventy-five
Ordinal75th
(seventy-fifth)
Factorization3 × 52
Divisors1, 3, 5, 15, 25, 75
Greek numeralΟΕ´
Roman numeralLXXV, lxxv
Binary10010112
Ternary22103
Senary2036
Octal1138
Duodecimal6312
Hexadecimal4B16

75 (seventy-five) is the natural number following 74 and preceding 76.


In mathematics

75 is a self number because there is no integer that added up to its own digits adds up to 75.[1][2] It is the sum of the first five pentagonal numbers, and therefore a pentagonal pyramidal number,[3][4] as well as a nonagonal number.[5][6]

It is also the fourth ordered Bell number,[7] and a Keith number, because it recurs in a Fibonacci-like sequence started from its base 10 digits: 7, 5, 12, 17, 29, 46, 75...[8][9]

A permutohedron on four elements, a three-dimensional convex polyhedron. It contains 24 vertices, 36 edges, and 14 two-dimensional faces, all of which together with the whole three-dimensional polyhedron equal to the 75 weak orderings on four elements.

75 is the count of the number of weak orderings on a set of four items.[10]

Excluding the infinite sets, there are 75 uniform polyhedra in the third dimension, which incorporate star polyhedra as well.[11] Inclusive of 7 families of prisms and antiprisms, there are also 75 uniform compound polyhedra.[12]

References

  1. Sloane, N. J. A. (ed.). "Sequence A003052". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. Weisstein, Eric W. "Self Number". mathworld.wolfram.com. Wolfram Research, Inc. Retrieved 2026-10-25.
  3. Sloane, N. J. A. (ed.). "Sequence A001106". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. Weisstein, Eric W. "Pentagonal Pyramidal Number". mathworld.wolfram.com. Wolfram Research, Inc. Retrieved 2026-10-25.
  5. Sloane, N. J. A. (ed.). "Sequence A002411". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. Weisstein, Eric W. "Nonagonal Number". mathworld.wolfram.com. Wolfram Research, Inc. Retrieved 2026-10-25.
  7. Sloane, N. J. A. (ed.). "Sequence A000670 (Fubini numbers: number of preferential arrangements of n labeled elements; or number of weak orders on n labeled elements; or number of ordered partitions of [n])". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2026-10-25.
  8. Klazar, Martin; Luca, Florian (2007). "Counting Keith Numbers". Journal of Integer Sequences. 10 (07.2.2): 2. Retrieved 2026-10-25.
  9. Sloane, N. J. A. (ed.). "Sequence A007629 (Keith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  10. Sloane, N. J. A. (ed.). "Sequence A000670". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  11. Sopov, S. P. (1970). "A proof of the completeness on the list of elementary homogeneous polyhedra". Ukrainskiui Geometricheskiui Sbornik (8): 139–156. MR 0326550.
  12. Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, 79 (3): 447–457, doi:10.1017/S0305004100052440, MR 0397554