225 (two hundred [and] twenty-five) is the natural number following 224 and preceding 226.
Number: | 225 |
Prime: | no |
225 is the smallest number that is a polygonal number in five different ways.[1] It is a square number,[2] an octagonal number,[3] and a squared triangular number .[4]
As the square of a double factorial, 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, 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]