This article is about the integer. For the year 7744, see 8th millennium

8th millennium

The eighth millennium is a period of time that will begin on January 1, 7001, and will end on December 31, 8000.-Astronomical events:All these dates are in a uniform time scale such as Terrestrial Time. When converted to our ordinary solar time or Universal Time, which is decidedly non-uniform, via...

.

Cardinal Cardinal number In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality of sets. The cardinality of a finite set is a natural number – the number of elements in the set. The transfinite cardinal numbers describe the sizes of infinite...	seven thousand seven hundred [and] forty-four
Ordinal Ordinal number In set theory, an ordinal number, or just ordinal, is the order type of a well-ordered set. They are usually identified with hereditarily transitive sets. Ordinals are an extension of the natural numbers different from integers and from cardinals...	7744th (seven thousand seven hundred [and] forty-fourth)
Factorization Factorization In mathematics, factorization or factoring is the decomposition of an object into a product of other objects, or factors, which when multiplied together give the original...
Divisor Divisor In mathematics, a divisor of an integer n, also called a factor of n, is an integer which divides n without leaving a remainder.-Explanation:... s	2, 4, 8, 11 11 (number) 11 is the natural number following 10 and preceding 12.Eleven is the first number which cannot be counted with a human's eight fingers and two thumbs additively. In English, it is the smallest positive integer requiring three syllables and the largest prime number with a single-morpheme name... , 16 16 (number) 16 is the natural number following 15 and preceding 17. 16 is a composite number, and a square number, being 42 = 4 × 4. It is the smallest number with exactly five divisors, its proper divisors being , , and .... , 22 22 (number) 22 is the natural number following 21 and preceding 23.- In mathematics :Twenty-two is an even composite number, its proper divisors being 1, 2 and 11.... , 32 32 (number) 32 is the natural number following 31 and preceding 33.-In mathematics:32 is the smallest number n with exactly 7 solutions to the equation φ = n... , 44 44 (number) 44 is the natural number following 43 and preceding 45.- In mathematics :Forty-four is a tribonacci number, a happy number, an octahedral number and a palindromic number.... , 64 64 (number) 64 is the natural number following 63 and preceding 65.-In mathematics:Sixty-four is the square of 8, the cube of 4, and the sixth power of 2. It is the smallest number with exactly seven divisors. It is the lowest positive power of two that is adjacent to neither a Mersenne prime nor a Fermat... , 88 88 (number) 88 is the natural number following 87 and preceding 89.- In mathematics :Eighty-Eight is a refactorable number, a primitive semiperfect number and an untouchable number... , 121 121 (number) 121 is the natural number following 120 and preceding 122.-In mathematics:One hundred [and] twenty-one is a square and is the sum of three consecutive primes . There are no squares besides 121 known to be of the form 1 + p + p^2 + p^3 + p^4, where p is prime... , 176 176 (number) 176 is the natural number following 175 and preceding 177.-In mathematics:* 176 is an even number* 176 is an abundant number, as 196 is greater than 176* 176 is a cake number* 176 is a composite number... , 242 242 (number) 242 is the natural number following 241 and preceding 243.-In mathematics:242 is the smallest integer to start a run of four consecutive integers with the same number of divisors.242 is a nontotient since there is no integer with 242 coprimes below it.... , 352, 484, 704, 968, 1,936, 3,872
Roman numeral	MMDCCXLIV
Binary Binary numeral system The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...	1111001000000
Octal Octal The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Numerals can be made from binary numerals by grouping consecutive binary digits into groups of three...	17100
Duodecimal Duodecimal The duodecimal system is a positional notation numeral system using twelve as its base. In this system, the number ten may be written as 'A', 'T' or 'X', and the number eleven as 'B' or 'E'...	4594
Hexadecimal Hexadecimal In mathematics and computer science, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F to represent values ten to fifteen...	1E40

7,744 is the natural number

Natural number

In mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...

 following 7,743 and preceding 7,745.

In mathematics

7,744 is the square

Square number

In mathematics, a square number, sometimes also called a perfect square, is an integer that is the square of an integer; in other words, it is the product of some integer with itself...

 of 88

88 (number)

88 is the natural number following 87 and preceding 89.- In mathematics :Eighty-Eight is a refactorable number, a primitive semiperfect number and an untouchable number...

. It is the smallest square number

Square number

In mathematics, a square number, sometimes also called a perfect square, is an integer that is the square of an integer; in other words, it is the product of some integer with itself...

 which has no isolated digits. It is also the fourth 1,292-gonal number.

88 and 7,744 form a unique pair. There appear to be no other squares which are composed of exactly two contiguous groups of multiple equal digits, that is, its digits form the pattern nnn...n mmm...m.

There are also very few squares with no unpaired digits: there are only 17 such numbers less than 10¹⁶. Ten of those numbers are squares containing 7,744; except for two, their square root

Square root

In mathematics, a square root of a number x is a number r such that r2 = x, or, in other words, a number r whose square is x...

s are all numbers containing 88. The other nine numbers contain 44 and the last two significant digits of their square roots are 62; the square of 62

62 (number)

62 is a natural number following 61 and preceding 63. It is a composite number with the divisors 2 and 31 being the eighteenth discreet semiprime. 62 has an aliquot sum of 34; itself a discrete semiprime, and the 10 member aliquot sequence . 62 is therefore the tenth member of the 7-aliquot tree...

, 3,844, is 28

28 (number)

28 is the natural number following 27 and preceding 29.-In mathematics:It is a composite number, its proper divisors being 1, 2, 4, 7, and 14....

 less than half of 7,744 and one of the two other four-digit

Four-letter word

The phrase four-letter word refers to a set of English-language words written with four letters which are considered profane, including common popular or slang terms for excretory functions, sexual activity and genitalia, and sometimes also certain terms relating to Hell and damnation when used...

 squares ending in 44 (the other one is 1,444, the square of 38

38 (number)

This article discusses the number thirty-eight. For the year 38 CE, see 38. For other uses of 38, see 38 38 is the natural number following 37 and preceding 39.-In mathematics:...

). Discarding multiples of ten, the number of squares is reduced to five, as shown by the following chart:

Base	Square
88	7,744
74,162	5,500,002,244
105,462	11,122,233,444
2,973,962	8,844,449,977,444
31,500,088	992,255,544,007,744

7,744 is a Harshad number

Harshad number

A Harshad number, or Niven number in a given number base, is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "Harshad" comes from the Sanskrit + , meaning joy-giver. The Niven...

 in base 10.