Number reference
225 explained.
225: two hundred twenty-five, composite, perfect square; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- two hundred twenty-five
- Classification
- composite
- Factors
- 1, 3, 5, 9, 15, 25, 45, 75, 225
- Prime factorization
- 3 × 3 × 5 × 5
- Square root
- 15
- Cube root
- 6.082202
- Binary
- 11100001
- Octal
- 341
- Hexadecimal
- E1
- Roman numeral
- CCXXV
- Digit sum
- 9
- Digital root
- 9
What makes 225 notable
- Perfect square. 225 = 15², so a square of side 15 has an area of 225.
225 in everyday use
Two hundred twenty-five is fifteen squared, and drivers see it every day without noticing: in a tyre marking such as 225/45 R17, the first number is the tread width in millimetres, and 225 is one of the most common sizes on family cars. A 225-square-foot room is fifteen feet on a side, and a quarter of an hour is 900 seconds, of which 225 is a quarter again. In Roman numerals it is CCXXV.
The number illustrates a theorem attributed to Nicomachus: the sum of the first n cubes equals the square of the nth triangular number. Here 1³ + 2³ + 3³ + 4³ + 5³ = 1 + 8 + 27 + 64 + 125 = 225, and 1 + 2 + 3 + 4 + 5 = 15. Factored it is 3² × 5², giving nine divisors. It is also the ninth octagonal number, one of the rare numbers that is both square and octagonal, and its digit sum is 9.
Nearby numbers
How to read this page
The factor list shows every way 225 splits into equal whole-number groups — 9 divisors in total. The prime factorisation is the compact form of that same information, and the base conversions restate 225 for contexts that do not use decimal.
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