840 (number)
| ||||
|---|---|---|---|---|
| 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, dcccxl | |||
| Binary | 11010010002 | |||
| Ternary | 10110103 | |||
| Senary | 35206 | |||
| Octal | 15108 | |||
| Duodecimal | 5A012 | |||
| Hexadecimal | 34816 | |||
840 (eight hundred [and] forty) is the natural number following 839 and preceding 841.
Mathematical properties
[edit]- It is an even number.
- It is a practical number.
- It is a congruent number.
- It is the 15th highly composite number,[1] with 32 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. Since the sum of its divisors (excluding the number itself) 2040 > 840
- It is an abundant number and also a superabundant number.[2]
- It is an idoneal number.[3]
- It is the least common multiple of the numbers from 1 to 8.[4]
- It is the smallest number divisible by every natural number from 1 to 10, except 9.
- It is the number under 1000 with the most divisors, at 32.
- It 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]
- It is an evil number.
- It is a palindrome number and a repdigit number repeated in the positional numbering system in base 29 (SS) and in that in base 34 (OO).
- It is the sum of a twin prime (419 + 421).
- It is the triple-digit number with the most divisors at 32.
References
[edit]- ^ 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.
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