Overview: 540 is a positive integer that follows 539 and precedes 541. In Roman numerals it is written DXL. Mathematically it is a composite number with multiple divisors and several notable arithmetic and geometric properties.
Algebraic and arithmetic properties
The prime factorization of 540 is 22·33·5. From this factorization come a number of standard functions: it has 24 positive divisors and the sum of all divisors σ(540) = 1680, giving an aliquot sum (proper divisors) of 1140, which makes 540 an abundant number. Its Euler totient φ(540) = 144.
540 is divisible by 9 (digital sum 5+4+0 = 9), so it is a Harshad number in base 10. In binary it is 1000011100 and in hexadecimal it is 0x21C.
Divisors
- 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20,
- 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540
Geometry and measures: 540 degrees appears often in planar geometry. It is the sum of the interior angles of a simple convex pentagon: for an n‑gon the interior sum is (n−2)·180°, so for n=5 this equals 540°. Also, a rotation of 540° corresponds to one and a half full revolutions (360° + 180°), a measure used informally in sports and performing arts to describe spins.
Historical and cultural notes: The number 540 may also be used as a calendar year label (540 BC or AD 540) in historical chronology. In modern popular culture the term "540" commonly denotes a 540° spin in skateboarding, snowboarding, BMX and similar disciplines, indicating one-and-a-half rotations.
Notable distinctions: Because 540 = 22·33·5, it is divisible by high powers of 3 (including 27) and by 4. Its totient value 144 is a perfect square (122), a fact sometimes highlighted in number‑theoretic observations. As an abundant, composite integer with many small prime factors, 540 serves as a useful example in elementary factorization and divisor-function exercises.