225 (number)

225 (two hundred [and] twenty five) is the natural number following 224 and preceding 226.

← 224 225 226 →
← 200 210 220 230 240 250 260 270 280 290 → List of numbers — Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	two hundred twenty-five
Ordinal	225th (two hundred and twenty-fifth)
Factorization	32× 52
Prime	no
Roman numeral	CCXXV
Binary	111000012
Ternary	221003
Quaternary	32014
Quinary	14005
Senary	10136
Octal	3418
Duodecimal	16912
Hexadecimal	E116
Vigesimal	B520
Base 36	6936

225 is the smallest number that is a polygonal number in five different ways. It is a square number (225 = 15²), an octagonal number, and a squared triangular number (225 = (1 + 2 + 3 + 4 + 5)² = 1³ + 2³ + 3³ + 4³ + 5³) .

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. And as one of the Stirling numbers of the first kind, it counts the number of permutations of six items with exactly three cycles.

225 is a highly composite odd number, meaning that it has more divisors than any smaller odd numbers. 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.

225 is the smallest square number to have one of every digit in some number base (225 is 3201 in base 4)