9768

9768 is a natural number that follows 9767 and precedes 9769. It is even and composite, and it appears in various mathematical contexts as a concrete example of an abundant number.

Mathematics: Prime factorization and divisors begin with 9768 = 2^3 × 3 × 11 × 37. This factorization yields 32 positive divisors. The number is divisible by several smaller integers, including 6, 8, 11, 12, 22, 24 and 44, among others, reflecting its composite structure.

Classification as abundant: The sum of all divisors of 9768, denoted sigma(9768), equals 27360. Subtracting the number itself gives the sum of proper divisors: 27360 − 9768 = 17592. Since 17592 exceeds 9768, the number is classified as abundant. Its abundance over itself is 7824, and the divisor-sum ratio sigma(9768)/9768 is approximately 2.80.

Representations: In different bases, 9768 is expressed as 0x2628 in hexadecimal and as 10011000101000 in binary. These representations help illustrate its structure relative to powers of two and to common computational formats.

Overall, 9768 serves as a representative example of an even, composite, and abundant integer with a known prime factorization and standard base representations.