840 (number)

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← 839 840 841 →
Cardinaleight hundred forty
Ordinal840th
(eight hundred fortieth)
Factorization23× 3 × 5 × 7
Divisors1, 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 numeralΩΜ´
Roman numeralDCCCXL
Binary11010010002
Ternary10110103
Quaternary310204
Quinary113305
Senary35206
Octal15108
Duodecimal5A012
Hexadecimal34816
Vigesimal22020
Base 36NC36

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[edit]

  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.