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Natural 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
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
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 the smallest number divisible by every natural number from 1 to 10, except 9.
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 and 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).
It is the sum of a twin prime (419 + 421).
References
^
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.
100,000
1,000,000
10,000,000
100,000,000
1,000,000,000