9855

← 9854 9855 9856 →
List of numbers Integers ← 0 1k 2k 3k 4k 5k 6k 7k 8k 9k →
Cardinal	nine thousand eight hundred fifty-five
Ordinal	9855th (nine thousand eight hundred fifty-fifth)
Factorization	33 × 5 × 73
Divisors	1, 3, 5, 9, 15, 27, 45, 73, 135, 219, 365, 657, 1095, 1971, 3285, 9855
Greek numeral	,ΘΩΝΕ´
Roman numeral	IXDCCCLV, ixdccclv
Binary	100110011111112
Ternary	1111120003
Senary	1133436
Octal	231778
Duodecimal	585312
Hexadecimal	267F16

9855 (nine thousand eight hundred fifty-five) is the natural number following 9854 and preceding 9856. An odd and composite number, its prime factors are 3, 5, and 73 and its prime factorization is:

${\displaystyle 9855=3^{3}\times 5\times 73}$.

It is the sum of all the numbers in any given row, column, or diagonal of the 27 × 27 magic square, ^{[1] [2]} as shown in the following calculation:

${\displaystyle 9855={\frac {1}{27}}\sum _{k=1}^{27^{2}}k={\frac {27\times (27^{2}+1)}{2}}}$

The 27 × 27 magic square contains 1 to 729, with 365 in the center. ^[2]

9855 is also the number of days in 27 years; C.A. Brown hypothesized in a 1906 edition of The Monist that this number could have held a significance for Ancient Greeks as the "dividing line between the ages when men and women should begin to bear children to the State, 20-27 years for women, 27-34 years for men" ^[2]

References

1. Square, The Magic. "The Magic Square Info". The Magic Square Info. Retrieved 2023-07-08.
2. Browne, C. A. (1906). "Magic Squares and Pythagorean Numbers" . The Monist. 16 (3): 422–433. doi:10.5840/monist190616319. ISSN   0026-9662. JSTOR   27899667.