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.[1]
Mathematical properties
[edit]- It is an even number.[2]
- It is a practical number.[2]
- It is a congruent number.
- It is a sparsely totient number[3]
- It is a Harshad number in base 2 through base 10
- It is a balanced number[4]
- It is the 15th highly composite number,[5] 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.[1] Since the sum of its divisors (excluding the number itself) 2040 > 840[6]
- It is an abundant number[1][6] and also a superabundant number.[7]
- It is an idoneal number.[8]
- It is the least common multiple of the numbers from 1 to 8.[9]
- It is the smallest number divisible by every natural number from 1 to 10, except 9.[2]
- 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.[10]
- It is an evil number.[2]
- It is a palindrome number and a repdigit number repeated in the positional numbering system in base 29 (SS) and in base 34 (OO).[6]
- It is the sum of a twin prime (419 + 421).
- It is the triple-digit number with the most divisors at 32.
- It is the smallest k such that the multiplicative group of integers modulo k is the direct product of 5 but no fewer cyclic groups.[2] (Here ). Equivalently, it is the least modulus with 25 square roots of 1.[11]
References
[edit]- 1 2 3 Vanovschi, Vitalii. "Properties of the number 840". www.numberempire.com. Retrieved 2026-09-18.
- 1 2 3 4 5 Khovanova, Tanya. "Properties of 840". Number Gossip. Retrieved 2026-09-18.
- ↑ Sloane, N. J. A. (ed.). "Sequence A036913 (Sparsely totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- ↑ Sloane, N. J. A. (ed.). "Sequence A020492 (Balanced numbers: numbers k such that phi(k) (A000010) divides sigma(k) (A000203))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ 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.
- 1 2 3 "The Positive Integer 20067". www.positiveintegers.org. Retrieved 2026-09-17.
- ↑ 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.
- ↑ Sloane, N. J. A. (ed.). "Sequence A102476 (Least modulus with 2^n square roots of 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
| |||||||||
| |||||||||
| |||||||||
| |||||||||
 | This article about a number is a stub. You can help Wikipedia by adding missing information. |