# 225 (number)

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

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Cardinal | two hundred twenty-five | |||

Ordinal |
225th (two hundred and twenty-fifth) | |||

Factorization |
3^{2}× 5^{2} | |||

Prime | no | |||

Roman numeral | CCXXV | |||

Binary |
11100001_{2} | |||

Ternary |
22100_{3} | |||

Quaternary |
3201_{4} | |||

Quinary |
1400_{5} | |||

Senary |
1013_{6} | |||

Octal |
341_{8} | |||

Duodecimal |
169_{12} | |||

Hexadecimal |
E1_{16} | |||

Vigesimal |
B5_{20} | |||

Base 36 |
69_{36} |

225 is the smallest number that is a polygonal number in five different ways.^{[1]} It is a square number (225 = 15^{2}),^{[2]}
an octagonal number,^{[3]} and a squared triangular number (225 = (1 + 2 + 3 + 4 + 5)^{2} = 1^{3} + 2^{3} + 3^{3} + 4^{3} + 5^{3}) .^{[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]}

## In other fields

- The years 225 and 225 BC
- .225 Winchester, firearm cartridge

## References

- ↑ "Sloane's A063778 : a(n) = the least integer that is polygonal in exactly n ways".
*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. - ↑ "Sloane's A000290 : The squares".
*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. - ↑ "Sloane's A000567 : Octagonal numbers".
*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. - ↑ "Sloane's A000537 : Sum of first n cubes; or n-th triangular number squared".
*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. - ↑ "Sloane's A001818 : Squares of double factorials".
*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. - ↑ "Sloane's A000399 : Unsigned Stirling numbers of first kind s(n,3)".
*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. - ↑ "Sloane's A053624 : Highly composite odd numbers".
*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. - ↑ "Sloane's A033632".
*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. - ↑ "Sloane's A033950 : Refactorable numbers".
*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. 2016-04-18. Retrieved 2016-04-18. - ↑ "Sloane's A061845 : Numbers which have one of every digit in some base".
*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation.