395 is the integer that follows 394 and precedes 396. As a counting number it appears in basic enumerations and as an identifier in many systems. Mathematically it is an odd composite number and, more specifically, a semiprime—the product of two prime numbers.
Mathematical properties
The prime factorization of 395 is 5 × 79, so its positive divisors are 1, 5, 79 and 395. Because the sum of its proper divisors (1 + 5 + 79 = 85) is less than 395, it is classified as a deficient number. Its Euler totient value, φ(395), equals 312, reflecting the count of integers less than 395 that are coprime to it. Numerically it lies between 19² (361) and 20² (400).
Numerical representations
395 can be expressed in several common numeral systems and notations:
- Decimal: 395
- Roman numerals: CCCXCV
- Binary: 110001011
- Hexadecimal: 0x18B
- Octal: 613
Year 395 (AD)
The year 395 AD is often noted in historical overviews because it marks a significant moment in late antiquity: the death of the Roman emperor Theodosius I and the effective permanent division of the Roman Empire into eastern and western administrations under his sons. That political change had long-term consequences for the late Roman world and the later histories of medieval Europe and Byzantium.
As with many three-digit numbers, 395 is commonly used as an identifier in catalogues, model numbers, route designations and scores. Its mathematical simplicity—being the product of a small and a larger prime—makes it a convenient example in elementary number theory exercises on factorization, divisors and totients.
Quick facts: it is odd, composite, semiprime and deficient. The number finds routine practical use as an index or label, while its appearance as a calendar year ties it to an important turning point in Roman imperial administration.