7700

7700 is a natural number that follows 7699 and precedes 7701. In mathematics, 7700 is an even composite number. Its prime factorization is 2^2 × 5^2 × 7 × 11, which means it has many divisors.

The number of positive divisors of 7700 is 36. The sum of all its divisors is 20832, so the sum of proper divisors (excluding 7700) is 13132, making 7700 an abundant number. Euler’s totient function value is φ(7700) = 2400, indicating the count of integers up to 7700 that are relatively prime to it.

Representations in common bases include decimal 7700, binary 1111000010100_2, hexadecimal 0x1E14, and octal 17024_8. Unusually, its decimal form is a round number composed as 77 × 100, reflecting a simple factorization pattern.

In broader contexts, 7700 is treated as a plain integer without notable named constants or widely cited theorems specifically associated with it. It can serve as a test or example value in teaching materials and in algorithms involving base conversion, factorization, or divisor calculations due to its small prime factors and multiple divisors.