thirty

Thirty is the natural number that comes after twenty-nine and before thirty-one. In decimal notation it is written as 30. It has several standard representations in different numeral systems: Roman numerals XXX, binary 11110, and hexadecimal 1E.

The word thirty originates from Old English þrītig, from Proto-Germanic *þrītigaz, formed by combining the word for three with a suffix indicating tens. This etymology ties the term to the idea of three tens.

In mathematics, thirty is the product of the first three primes: 2 × 3 × 5. It has eight positive divisors: 1, 2, 3, 5, 6, 10, 15, and 30. It is the least common multiple of 2, 3, and 5. Thirty is an even, composite number, and its Euler’s totient is φ(30) = 8.

Usage and occurrencewise, thirty appears in several practical contexts. Many calendars designate April, June, September, and November as the months with 30 days; February has 28 days in common years and 29 in leap years. In timekeeping, 30 minutes equals half an hour, and 30 seconds equals half a minute. The element zinc has atomic number 30, and is used in galvanization and various alloys. Culturally, thirty is often seen as a milestone age in adulthood and a common reference point for spans of decades.