|
720 (number)
720 (seven hundred [and] twenty) is the natural number following 700 (number)#710s, 719 and preceding 700 (number)#720s, 721. It is 6! (6 (number), 6 factorial), a composite number with thirty divisors, more than any number below, making it a highly composite number. It is a Harshad number in every base from binary to decimal. 720 is expressible as the product of consecutive integers in two different ways: , and . There are 49 solutions to the equation Euler's totient function, φ(''x'') = 720, more than any integer below it, making 720 a highly totient number. 720 is a 241-polygonal number, gonal number. In other fields 720 is: * A common vertical display resolution for High-definition television, HDTV (see 720p). * 720° is two full rotations; the term "720" refers to a skateboarding trick. * 720° is also the name of a skateboarding video game. * 720 is a dual area codes 303 and 720, area code in the Denver Metro Area along with 303. * 720° is the sum of all the defect ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1 (number)
1 (one, unit, unity) is a number representing a single or the only entity. 1 is also a numerical digit and represents a single unit of counting or measurement. For example, a line segment of ''unit length'' is a line segment of length 1. In conventions of sign where zero is considered neither positive nor negative, 1 is the first and smallest positive integer. It is also sometimes considered the first of the infinite sequence of natural numbers, followed by 2, although by other definitions 1 is the second natural number, following 0. The fundamental mathematical property of 1 is to be a multiplicative identity, meaning that any number multiplied by 1 equals the same number. Most if not all properties of 1 can be deduced from this. In advanced mathematics, a multiplicative identity is often denoted 1, even if it is not a number. 1 is by convention not considered a prime number; this was not universally accepted until the mid-20th century. Additionally, 1 is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
40 (number)
40 (forty) is the natural number following 39 and preceding 41. Though the word is related to "four" (4), the spelling "forty" replaced "fourty" in the course of the 17th century and is now the standard form. In mathematics *Forty is a composite number, a refactorable number, an octagonal number, and—as the sum of the first four pentagonal numbers: 1 + 5 + 12 + 22 =40—it is a pentagonal pyramidal number. Adding up some subsets of its divisors (e.g., 1, 4, 5, 10, and 20) gives 40; hence, 40 is a semiperfect number. *Given 40, the Mertens function returns 0. 40 is the smallest number with exactly nine solutions to the equation Euler's totient function \varphi (x)=n. *Forty is the number of -queens problem solutions for n=7. *Forty is a repdigit in ternary (1111, ''i.e.'', 3^ + 3^ + 3^ + 3^, or, in other words, \frac ) and a Harshad number in decimal. In science *The atomic number of zirconium. *Negative forty is the unique temperature at which the Fahrenheit and Celsius ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
700 (number)
700 (seven hundred) is the natural number following 699 and preceding 701. It is the sum of four consecutive primes (167 + 173 + 179 + 181), the perimeter of a Pythagorean triangle (75 + 308 + 317) and a Harshad number. Integers from 701 to 799 Nearly all of the palindromic integers between 700 and 800 are used as model numbers for Boeing Commercial Airplanes, and the only one not officially used by Boeing, 797, is commonly speculated to be the number of the next new Boeing commercial airplane. 700s * 701 = prime number, sum of three consecutive primes (229 + 233 + 239), Chen prime, Eisenstein prime with no imaginary part * 702 = 2 × 33 × 13, pronic number, nontotient, Harshad number * 703 = 19 × 37, triangular number, hexagonal number, smallest number requiring 73 fifth powers for Waring representation, Kaprekar number, area code for Northern Virginia along with 571, a number commonly found in the formula for body mass index * 704 = 26 × 11, Harshad number, lazy caterer nu ... [...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] |
360 (number)
360 (three hundred sixty) is the natural number following 359 and preceding 361. In mathematics *The divisors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 and 360, making a total of 24 divisors. *360 is a highly composite number. Not only is 360 highly composite, but it is also one of only 7 numbers such that no number less than twice as much has more divisors; the others are 1, 2, 6, 12, 60, and 2520. . 360 is also a superior highly composite number, a colossally abundant number, a refactorable number and a 5-smooth number. *360 is the smallest number divisible by every natural number from 1 to 10 except 7. *One of 360's divisors is 72, which is the number of primes below it. *The sum of Euler's totient function φ(x) over the first thirty-four integers is 360. *A circle is divided into 360 degrees for the purpose of angular measurement. 360° = 2 π rad is also called a round angle. This choice of unit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
240 (number)
240 (two hundred ndforty) is the natural number following 239 and preceding 241. In mathematics 240 is: *a semiperfect number. *a concatenation of two of its proper divisors. *a highly composite number since it has 20 divisors total (1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, and 240), more than any previous number. *a refactorable number or tau number, since it has 20 divisors and 20 divides 240. *a highly totient number, since it has 31 totient answers, more than any previous integer. *a pronic number since it can be expressed as the product of two consecutive integers, 15 and 16. *palindromic in bases 19 (CC19), 23 (AA23), 29 (8829), 39 (6639), 47 (5547) and 59 (4459). *a Harshad number in bases 2, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 15 (and 73 other bases). *the aliquot sum of 120 and 57121. *part of the 12161-aliquot tree. The aliquot sequence starting at 120 is: 120, 240, 504, 1056, 1968, 3240, 7650, 14112, 32571, 27333, 12161, 1, 0. 240 is the sm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
180 (number)
180 (one hundred ndeighty) is the natural number following 179 and preceding 181. In mathematics 180 is an abundant number, with its proper divisors summing up to 366. 180 is also a highly composite number, a positive integer with more divisors than any smaller positive integer. One of the consequences of 180 having so many divisors is that it is a practical number, meaning that any positive number smaller than 180 that is not a divisor of 180 can be expressed as the sum of some of 180's divisors. 180 is a Harshad number and a refactorable number. 180 is the sum of two square numbers: 122 + 62. It can be expressed as either the sum of six consecutive prime numbers: 19 + 23 + 29 + 31 + 37 + 41, or the sum of eight consecutive prime numbers: 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37. 180 is an Ulam number, which can be expressed as a sum of earlier terms in the Ulam sequence only as 177 + 3. 180 is a 61- gonal number. Half a circle has 180 degrees, and thus a U-turn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
144 (number)
144 (one hundred ndforty-four) is the natural number following 143 and preceding 145. 144 is a dozen dozens, or one gross. In mathematics 144 is the twelfth Fibonacci number, and the largest one to also be a square, as the square of 12 (which is also its index in the Fibonacci sequence), following 89 and preceding 233. 144 is the smallest number with exactly 15 divisors, but it is not highly composite since the smaller number 120 has 16 divisors. 144 is divisible by the value of its φ function, which returns 48 in this case. Also, there are 21 solutions to the equation φ(''x'') = 144, more than any integer below 144, making it a highly totient number. 144 = 27 + 84 + 110 + 133, the smallest number whose fifth power is a sum of four (smaller) fifth powers. This solution was found in 1966 by L. J. Lander and T. R. Parkin, and disproved Euler's sum of powers conjecture. 144 is in base 10 a sum-product number, as well as the sum of a twin prime pair (71 + 73). The maximum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
120 (number)
120, read as one hundred ndtwenty, is the natural number following 119 and preceding 121. In the Germanic languages, the number 120 was also formerly known as "one hundred". This "hundred" of six score is now obsolete, but is described as the long hundred or great hundred in historical contexts. In mathematics 120 is * the factorial of 5 i.e. 5 × 4 × 3 × 2 × 1 * the fifteenth triangular number, as well as the sum of the first eight triangular numbers, making it also a tetrahedral number. 120 is the smallest number to appear six times in Pascal's triangle (as all triangular and tetragonal numbers appear in it). Because 15 is also triangular, 120 is a doubly triangular number. 120 is divisible by the first 5 triangular numbers and the first 4 tetrahedral numbers. It is the eighth hexagonal number. * highly composite, superior highly composite, superabundant, and colossally abundant number, with its 16 divisors being more than any number lower than it has, and it is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
90 (number)
90 (ninety) is the natural number preceded by 89 and followed by 91. In the English language, the numbers 90 and 19 are often confused, as they sound very similar. When carefully enunciated, they differ in which syllable is stressed: 19 /naɪnˈtiːn/ vs 90 /ˈnaɪnti/. However, in dates such as 1999, and when contrasting numbers in the teens and when counting, such as 17, 18, 19, the stress shifts to the first syllable: 19 /ˈnaɪntiːn/. In mathematics 90 is a pronic number, as it is the product of 9 and 10. It is nontotient, and divisible by the sum of its base 10 digits, which makes it a Harshad number. *It is the third unitary perfect number, since it is the sum of its unitary divisors excluding itself, and because it is equal to the sum of a subset of its divisors, it is also a semiperfect number. *90 is a Stirling number of the second kind S(n,k) from a n of 6 and a k of 3, as it is the number of ways of dividing a set of six objects into three non empty subsets. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
80 (number)
80 (eighty) is the natural number following 79 and preceding 81. In mathematics 80 is: * the sum of Euler's totient function φ(''x'') over the first sixteen integers. * a semiperfect number, since adding up some subsets of its divisors (e.g., 1, 4, 5, 10, 20 and 40) gives 80. * a ménage number. * palindromic in bases 3 (22223), 6 (2126), 9 (889), 15 (5515), 19 (4419) and 39 (2239). * a repdigit in bases 3, 9, 15, 19 and 39. The Pareto principle (also known as the 80-20 rule) states that, for many events, roughly 80% of the effects come from 20% of the causes... Every solvable configuration of the 15 puzzle can be solved in no more than 80 single-tile moves.A. Brüngger, A. Marzetta, K. Fukuda and J. NievergeltThe parallel search bench ZRAM and its applications ''Annals of Operations Research'' 90 (1999), pp. 45–63. In science * The atomic number of mercury In religion * According to Exodus 7:7, Moses was 80 years old when he initially spoke to Pharaoh o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
72 (number)
72 (seventy-two) is the natural number following 71 and preceding 73. It is half a gross or 6 dozen (i.e., 60 in duodecimal). In mathematics Seventy-two is a pronic number, as it is the product of 8 and 9. 72 is an abundant number, with a total of 12 factors, and a Euler totient of 24. 72 is also a highly totient number, as there are 17 solutions to the equation φ(''x'') = 72, more than any integer below 72. It is equal to the sum the sum of its preceding smaller highly totient numbers 24 and 48, and contains the first six highly totient numbers 1, 2, 4, 8, 12 and 24 as a subset of its proper divisors. 144, or twice 72, is also highly totient, as is 576, the square of 24. While 17 different integers have a totient value of 72, the sum of Euler's totient function φ(''x'') over the first 15 integers is 72. 72 is also a Harshad number in decimal, as it is divisible by the sum of its digits. *72 is the smallest Achilles number, as it's a powerful number that is not itself a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
