| ||||
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Cardinal | eight hundred forty | |||

Ordinal | 840th (eight hundred fortieth) | |||

Factorization | 2^{3}× 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 | 1101001000_{2} | |||

Ternary | 1011010_{3} | |||

Quaternary | 31020_{4} | |||

Quinary | 11330_{5} | |||

Senary | 3520_{6} | |||

Octal | 1510_{8} | |||

Duodecimal | 5A0_{12} | |||

Hexadecimal | 348_{16} | |||

Vigesimal | 220_{20} | |||

Base 36 | NC_{36} |

**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

**^**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.**^**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.**^**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.**^**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.**^**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.