4928

4928 is a natural number sitting between 4927 and 4929. It is even and composite. The prime factorization is 2^6 × 7 × 11, so 4928 equals 64 × 77. This factorization implies that the number has 28 positive divisors and is divisible by 2, 4, 8, 16, 32, and 64, as well as by 7 and 11.

In terms of divisor sums, the sum of all positive divisors of 4928 is 12,192, which means the sum of its proper divisors is 7,264. Since the sum of proper divisors exceeds the number itself, 4928 is classified as an abundant number. Its greatest power-of-two factor is 2^6, and it can be expressed as the product 64 × 77, highlighting its decomposition into coprime components 64 and 77.

4928 can be represented in several common bases. In binary it is 1001101000000, in hexadecimal it is 0x1340, and in octal it is 11500. The decimal digit sum is 4 + 9 + 2 + 8 = 23, and 4928 is not a Harshad number since it is not divisible by 23. Its modular properties include being congruent to 2 modulo 3 and congruent to 3 modulo 5, among others.

As a mathematical entity, 4928 serves as an example of a highly composite structure arising from the combination 2^6 with two odd primes, illustrating concepts such as divisor counting, abundance, and base representations without tying the number to a specific historical or cultural context.