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693 (number)
693 (six hundred ndninety-three) is the natural number following 692 and preceding 694. In mathematics 693 has twelve divisors: 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, and 693. Thus, 693 is tied with 315 for the highest number of divisors for any odd natural number below 900. The smallest positive odd integer with more divisors is 945, which has 16 divisors. Consequently, 945 is also the smallest odd abundant number, having an abundancy index of 1920/945 ≈ 2.03175. 693 appears as the first three digits after the decimal point in the decimal form for the natural logarithm of 2. To 10 digits, this number is 0.6931471805. As a result, if an event has a constant probability Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speakin ... of 0.1% of occurring, 693 is the smallest number of tria ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''Cardinal number, cardinal numbers'', and numbers used for ordering are called ''Ordinal number, ordinal numbers''. Natural numbers are sometimes used as labels, known as ''nominal numbers'', having none of the properties of numbers in a mathematical sense (e.g. sports Number (sports), jersey numbers). Some definitions, including the standard ISO/IEC 80000, ISO 80000-2, begin the natural numbers with , corresponding to the non-negative integers , whereas others start with , corresponding to the positive integers Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, while in other writings, that term is used instead for the integers (including negative integers). The natural ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
692 (number)
600 (six hundred) is the natural number following 599 and preceding 601. Mathematical properties Six hundred is a composite number, an abundant number, a pronic number and a Harshad number. Credit and cars * In the United States, a credit score of 600 or below is considered poor, limiting available credit at a normal interest rate. * NASCAR runs 600 advertised miles in the Coca-Cola 600, its longest race. * The Fiat 600 is a car, the SEAT 600 its Spanish version. Integers from 601 to 699 600s * 601 = prime number, centered pentagonal number * 602 = 2 × 7 × 43, nontotient, number of cubes of edge length 1 required to make a hollow cube of edge length 11, area code for Phoenix, AZ along with 480 and 623 * 603 = 32 × 67, Harshad number, Riordan number, area code for New Hampshire * 604 = 22 × 151, nontotient, totient sum for first 44 integers, area code for southwestern British Columbia (Lower Mainland, Fraser Valley, Sunshine Coast and Sea to Sky) * 605 = 5 × 112, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
694 (number)
600 (six hundred) is the natural number following 599 and preceding 601. Mathematical properties Six hundred is a composite number, an abundant number, a pronic number and a Harshad number. Credit and cars * In the United States, a credit score of 600 or below is considered poor, limiting available credit at a normal interest rate. * NASCAR runs 600 advertised miles in the Coca-Cola 600, its longest race. * The Fiat 600 is a car, the SEAT 600 its Spanish version. Integers from 601 to 699 600s * 601 = prime number, centered pentagonal number * 602 = 2 × 7 × 43, nontotient, number of cubes of edge length 1 required to make a hollow cube of edge length 11, area code for Phoenix, AZ along with 480 and 623 * 603 = 32 × 67, Harshad number, Riordan number, area code for New Hampshire * 604 = 22 × 151, nontotient, totient sum for first 44 integers, area code for southwestern British Columbia (Lower Mainland, Fraser Valley, Sunshine Coast and Sea to Sky) * 605 = 5 × 112, Harsha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
315 (number)
300 (three hundred) is the natural number following 299 and preceding 301. Mathematical properties The number 300 is a triangular number and the sum of a pair of twin primes (149 + 151), as well as the sum of ten consecutive primes (13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47). It is palindromic in 3 consecutive bases: 30010 = 6067 = 4548 = 3639, and also in base 13. Factorization is 30064 + 1 is prime Other fields Three hundred is: * In bowling, a perfect score, achieved by rolling strikes in all ten frames (a total of twelve strikes) * The lowest possible Fair Isaac credit score * Three hundred ft/s is the maximum legal speed of a shot paintball * In the Hebrew Bible, the size of the military force deployed by the Israelite judge Gideon against the Midianites () * According to Islamic tradition, 300 is the number of ancient Israeli king Thalut's soldiers victorious against Goliath's soldiers * According to Herodotus, 300 is the number of ancient Spar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abundant Number
In number theory, an abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number. The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16. The amount by which the sum exceeds the number is the abundance. The number 12 has an abundance of 4, for example. Definition A number ''n'' for which the ''sum'' ''of'' ''divisors'' ''σ''(''n'') > 2''n'', or, equivalently, the sum of proper divisors (or aliquot sum) ''s''(''n'') > ''n''. Abundance is the value ''σ''(''n'') − ''2n'' (or ''s''(''n'') − ''n''). Examples The first 28 abundant numbers are: :12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 108, 112, 114, 120, ... . For example, the proper divisors of 24 are 1, 2, 3, 4, 6, 8, and 12, whose sum is 36. Because 36 is greater than 24, the number 24 is abundant. Its abundance is 36 − 24 = 12. Prope ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Logarithm Of 2
The decimal value of the natural logarithm of 2 is approximately :\ln 2 \approx 0.693\,147\,180\,559\,945\,309\,417\,232\,121\,458. The logarithm of 2 in other bases is obtained with the formula :\log_b 2 = \frac. The common logarithm in particular is () :\log_ 2 \approx 0.301\,029\,995\,663\,981\,195. The inverse of this number is the binary logarithm of 10: : \log_2 10 =\frac \approx 3.321\,928\,095 (). By the Lindemann–Weierstrass theorem, the natural logarithm of any natural number other than 0 and 1 (more generally, of any positive algebraic number other than 1) is a transcendental number. Series representations Rising alternate factorial :\ln 2 = \sum_^\infty \frac=1-\frac12+\frac13-\frac14+\frac15-\frac16+\cdots. This is the well-known "alternating harmonic series". :\ln 2 = \frac +\frac\sum_^\infty \frac. :\ln 2 = \frac +\frac\sum_^\infty \frac. :\ln 2 = \frac +\frac\sum_^\infty \frac. :\ln 2 = \frac +\frac\sum_^\infty \frac. :\ln 2 = \frac +\frac\sum_^\infty \frac. : ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th Ed, (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', (Vol 1), 3rd Ed, (1968), Wiley, . The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lowest Common Multiple
In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers ''a'' and ''b'', usually denoted by lcm(''a'', ''b''), is the smallest positive integer that is divisible by both ''a'' and ''b''. Since division of integers by zero is undefined, this definition has meaning only if ''a'' and ''b'' are both different from zero. However, some authors define lcm(''a'',0) as 0 for all ''a'', since 0 is the only common multiple of ''a'' and 0. The lcm is the "lowest common denominator" (lcd) that can be used before fractions can be added, subtracted or compared. The least common multiple of more than two integers ''a'', ''b'', ''c'', . . . , usually denoted by lcm(''a'', ''b'', ''c'', . . .), is also well defined: It is the smallest positive integer that is divisible by each of ''a'', ''b'', ''c'', . . . Overview A multiple of a number is the product of that number and an integer. For example, 10 is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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