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840 (number) - Wikipedia
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Natural number
← 839 840 841 → 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.
Mathematical properties[edit]
- 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 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.
- ^ 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.
Integers −1 0s
100s
200s
300s
400s
500s
600s
700s
800s
900s
1000s
- 100,000
- 1,000,000
- 10,000,000
- 100,000,000
- 1,000,000,000
- 10,000,000,000
- 100,000,000,000
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