840 (number)
Natural number
From Wikipedia, the free encyclopedia
840 (eight hundred [and] forty) is the natural number following 839 and preceding 841.
Cardinaleight hundred forty
Ordinal840th
(eight hundred fortieth)
(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
| ||||
|---|---|---|---|---|
| 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 | |||
Mathematical properties
- 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 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.
- 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. (Here ). Equivalently, it is the least modulus with 25 square roots of 1.[6]
