8280

8280 is a natural number that follows 8279 and precedes 8281. In mathematics it is an even composite integer with several notable divisibility properties and arithmetic relations.

Prime factorization and divisors: 8280 = 2^3 * 3^2 * 5 * 23. From this factorization, the number of positive divisors is (3+1)(2+1)(1+1)(1+1) = 48, so 8280 has 48 divisors in total.

Divisibility and representations: The number is divisible by 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, and 360, among others. The sum of its digits is 8+2+8+0 = 18, so 8280 is a Harshad (Niven) number since 8280/18 = 460. Its digital root is 9, reflecting divisibility by 9.

Algebraic properties: 8280 is a multiple of 360, since 8280 = 360 × 23. The sum of all positive divisors is sigma(8280) = 28,080, making the sum of proper divisors equal to 19,800. Therefore, 8280 is an abundant number (the sum of its proper divisors exceeds the number itself). Euler’s totient function yields φ(8280) = 2,112.

Numerical representations: In binary, 8280 is 10000001011000. This and other base representations reflect the same underlying value in different numeral systems.

In summary, 8280 is a highly composite-looking yet standard composite number with a rich set of divisibility and arithmetic characteristics.