840 (number)

← 839 840 841 →
Cardinal eight hundred forty
Ordinal 840th
(eight hundred fortieth)
Factorization 23× 3 × 5 × 7
Divisors 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
Greek numeral ΩΜ´
Roman numeral DCCCXL
Binary 11010010002
Ternary 10110103
Quaternary 310204
Quinary 113305
Senary 35206
Octal 15108
Duodecimal 5A012
Hexadecimal 34816
Vigesimal 22020
Base 36 NC36

840 is the natural number following 839 and preceding 841.

It is a highly composite number,[1] a superabundant number,[2] an idoneal number,[3] and is the least common multiple of 1, 2, 3, 4, 5, 6, 7, 8.[4]

840 is the largest number k such that all coprime quadratic residues modulo k are squares. In this case, they are 1, 121, 169, 289, 361 and 529.[5]

References

  1. ↑ Sloane, N.J.A. (ed.). "Sequence A002182 (Highly composite numbers, definition (1): where d(n), the number of divisors of n (A000005), increases to a record)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ↑ Sloane, N.J.A. (ed.). "Sequence A004394 (Superabundant [or super-abundant] numbers: n such that sigma(n)/n > sigma(m)/m for all m<n, sigma(n) being the sum of the divisors of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ↑ Sloane, N.J.A. (ed.). "Sequence A000926 (Euler's "numerus idoneus" (or "numeri idonei", or idoneal, or suitable, or convenient numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ↑ Sloane, N.J.A. (ed.). "Sequence A003418 (Least common multiple (or LCM) of {1, 2, ..., n} for n >= 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ↑ Sloane, N.J.A. (ed.). "Sequence A303704 (Numbers k such that all coprime quadratic residues modulo k are squares.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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