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Natural number From Wikipedia, the free encyclopedia
225 (two hundred [and] twenty-five) is the natural number following 224 and preceding 226.
| ||||
---|---|---|---|---|
Cardinal | two hundred twenty-five | |||
Ordinal | 225th (two hundred twenty-fifth) | |||
Factorization | 32 × 52 | |||
Prime | no | |||
Greek numeral | ΣΚΕ´ | |||
Roman numeral | CCXXV | |||
Binary | 111000012 | |||
Ternary | 221003 | |||
Senary | 10136 | |||
Octal | 3418 | |||
Duodecimal | 16912 | |||
Hexadecimal | E116 |
225 is the smallest number that is a polygonal number in five different ways.[1] It is a square number (225 = 152),[2] an octagonal number,[3] and a squared triangular number (225 = (1 + 2 + 3 + 4 + 5)2 = 13 + 23 + 33 + 43 + 53) .[4]
As the square of a double factorial, 225 = 5!!2 counts the number of permutations of six items in which all cycles have even length, or the number of permutations in which all cycles have odd length.[5] And as one of the Stirling numbers of the first kind, it counts the number of permutations of six items with exactly three cycles.[6]
225 is a highly composite odd number, meaning that it has more divisors than any smaller odd numbers.[7] After 1 and 9, 225 is the third smallest number n for which σ(φ(n)) = φ(σ(n)), where σ is the sum of divisors function and φ is Euler's totient function.[8] 225 is a refactorable number.[9]
225 is the smallest square number to have one of every digit in some number base (225 is 3201 in base 4) [10]
225 is the first odd number with exactly 9 divisors.[11]
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