840 (number)

840 is the natural number following 839 and preceding 841.

← 839 840 841 →
List of numbers — Integers ← 0 100 200 300 400 500 600 700 800 900 →
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	11010010002
Ternary	10110103
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 a 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 1, 2, 3, 4, 5, 6, 7, 8.[4]
• 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).

References

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.