840 (number)

← 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	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

Last updated March 13, 2025

840 (eight hundred [and] forty) is the natural number following 839 and preceding 841.

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 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

↑ Sloane, N. J. A. (ed.). "SequenceA002182(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.). "SequenceA004394(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.). "SequenceA000926(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.). "SequenceA003418(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.). "SequenceA303704(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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[1] Sloane, N. J. A. (ed.). "SequenceA002182(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.). "SequenceA004394(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.). "SequenceA000926(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.). "SequenceA003418(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.). "SequenceA303704(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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