Overview. Twenty-one is the integer that follows twenty and precedes twenty-two. As a member of the natural numbers it is commonly written in words as "twenty-one" and in numerals as 21. It is an odd, composite number and appears in many everyday contexts and structured systems across mathematics, science and culture. For a basic reference see general number.
Mathematical properties
Numerically, 21 has several simple and instructive features. It factors as 3 × 7, so it is a semiprime (a product of two primes) and its positive divisors are listed below. It is a triangular number (the sixth triangular number, since 1+2+3+4+5+6 = 21) and also appears in the Fibonacci sequence (..., 8, 13, 21, 34, ...).
- Divisors: 1, 3, 7, 21. See basic divisor information at divisibility.
- Parity: odd number (odd).
- Binary and other bases: 21 = 10101₂ = 25₈ = 15₁₆.
- Digit-sum properties: 2+1 = 3, and 21 is divisible by 3, so it is a Harshad number in base 10.
Notation and symbols
Common notations include the Roman numeral form XXI and the Greek numeral form κα (kappa + alpha). In algebraic and number-theory contexts 21 is used as a simple example of a composite, semiprime, and triangular integer.
Roman: XXI. Greek: κα.
Uses, examples and cultural notes
Twenty-one appears in a variety of social and cultural roles. The card game commonly known as "Twenty-One" or "blackjack" centers on reaching a hand value of 21, and is one of the best-known gambling games worldwide (card game). In several countries age-related legal thresholds use 21: for example, in the United States the legal minimum age to purchase and publicly consume alcoholic beverages is 21 in most jurisdictions (legal drinking age).
Science and notable facts
In chemistry, the atomic number 21 identifies the element scandium, which has 21 protons in its nucleus. Twenty-one also appears in ceremonial contexts, such as the 21-gun salute used in state honors. Mathematically it provides a compact example for teaching factorization, divisibility rules, and sequences like triangular and Fibonacci numbers.
Distinctions and quick facts:
- Semiprime and product of two distinct primes (3 and 7).
- Triangular and Fibonacci—an intersection that makes it useful pedagogically.
- Expressed as XXI in Roman numerals and κα in Greek numerals.
- Appears in games, legal age limits, and as the atomic number of scandium.
For concise introductions or public-facing summaries about numbers and their cultural roles, consult general references and educational materials: number overview, parity, and resources on card games and legal ages at Twenty-One (game) and age 21 regulations. For numeral systems see notes on Roman numerals at Roman notation.