1160 (number)

Arithmetic properties

From the factorization 2^3·5·29 we obtain several standard invariants. 1160 has (3+1)(1+1)(1+1) = 16 positive divisors. The sum of all divisors σ(1160) = 2700, so the sum of proper divisors is 2700 − 1160 = 1540; because this exceeds 1160 the number is classified as abundant. The Euler totient function is φ(1160) = 448.

• Prime factors: 2, 5, 29
• Number of divisors: 16
• Sum of divisors (σ): 2700
• Proper divisor sum (aliquot): 1540 (abundant)
• Euler totient (φ): 448

Divisors

The complete set of positive divisors can be listed explicitly. All divisors of 1160 are:

• 1, 2, 4, 5, 8, 10, 20, 29, 40, 58, 116, 145, 232, 290, 580, 1160

Representations and notable forms

1160 admits several simple representations and notations used in mathematics and everyday contexts. In binary it is 10010001000, in hexadecimal 0x488, and in Roman numerals MCLX. Because the sum of its decimal digits is 8 and 1160 is divisible by 8, it is a Harshad (Niven) number in base 10.

Arithmetic identities include a sum of two squares: 1160 = 34^2 + 2^2 = 1156 + 4. That follows from its prime factors, since all primes congruent to 3 (mod 4) appear with even exponent (in fact none appear here), so it can be expressed as a sum of two integer squares.

Context and remarks

Beyond pure number theory, the symbol "1160" commonly appears as a year label (1160 AD or 1160 BC) in historical chronologies, as an identifier in catalogs or model numbers, and in measurements where a round multiple of 10 is convenient. As an integer it illustrates how prime factor structure controls divisor behavior, representability as sums of squares, and multiplicative arithmetic functions.