7744
 |
- This article is about the integer. For the year 7745, see 8th millennium.
| Template:Numbers 1000-10000 | |
| Cardinal | seven thousand seven hundred [and] forty-four |
| Ordinal | 7744th (seven thousand seven hundred [and] forty-fourth) |
| Factorization | |
| Divisors | 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 121, 176, 242, 352, 484, 704, 968, 1,936, 3,872 |
| Roman numeral | VMMDCCXLIV |
| Binary | 1111001000000 |
| Octal | 17100 |
| Duodecimal | 4594 |
| Hexadecimal | 1E40 |
7,744 is the natural number following 7,743 and preceding 7,745.
In mathematics
7,744 is the square of 88. It is the smallest square number 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 roots 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, 3,844, is 28 less than half of 7,744 and one of the two other four-digit squares ending in 44 (the other one is 1,444, the square of 38). 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 in base 10.