85 is the integer that follows eighty-four and precedes eighty-six. As a whole number it is odd and occupies a familiar place in counting, labeling, and measurement. The numeral itself — 85 — appears often in calendars, ages, addresses, and catalog numbers, but it also has specific mathematical characteristics discussed below.
Mathematical properties
Numerically, 85 is a composite number and more precisely a semiprime because it factors as the product of two primes: 5 and 17. Its positive divisors are listed here:
The sum of all divisors (the sigma function) is 1 + 5 + 17 + 85 = 108, while the sum of proper divisors (the aliquot sum) is 23, so 85 is a deficient number. Euler's totient function yields φ(85) = φ(5)·φ(17) = 4·16 = 64.
In several common representations 85 shows simple patterns: in binary it is 1010101 (a repeating 1–0 pattern), and in Roman numerals it is written LXXXV. It can also be expressed as the sum of two squares: 85 = 7² + 6².
Context, uses, and examples
Outside pure number theory, 85 appears in ordinary contexts such as ages, anniversaries, route numbers, and ratings. In science, atomic number 85 corresponds to the element astatine, linking the integer to chemistry and the periodic table. In computing and communications, bit patterns and byte values sometimes use 85 for illustrative examples because of its alternating binary pattern.
As a semiprime, 85 serves as a simple example in elementary cryptography and factorization exercises. Its totient value, 64, which is a power of two, makes modular arithmetic modulo 85 convenient for certain illustrative group-theory examples in classrooms.
Notable distinctions: 85 is composite but not a perfect power, not a square, and not a member of several special prime-derived classes (for example, it is not a Blum integer). Its simple factorization and representational properties make it a useful, easily understood example across arithmetic, number theory, and applied examples.