Number reference
21 explained.
21: twenty-one, composite, triangular number; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- twenty-one
- Classification
- composite
- Factors
- 1, 3, 7, 21
- Prime factorization
- 3 × 7
- Square root
- 4.582576
- Cube root
- 2.758924
- Binary
- 10101
- Octal
- 25
- Hexadecimal
- 15
- Roman numeral
- XXI
- Digit sum
- 3
- Digital root
- 3
What makes 21 notable
- Triangular number. 21 is the 6th triangular number: it is the sum 1 + 2 + … + 6, the count of items in a triangle with 6 rows.
- Fibonacci number. 21 appears in the Fibonacci sequence, where each term is the sum of the two before it.
21 in everyday use
Twenty-one is the target in blackjack, the legal drinking age across the United States since 1984, and the atomic number of scandium. Twenty-one guns fire in the highest military salute, and the twenty-first century began in 2001. The pips on a standard die total twenty-one: 1 + 2 + 3 + 4 + 5 + 6. In the game of table tennis matches were played to 21 points until the rules changed to 11 in 2001.
Twenty-one is the sixth triangular number and the eighth Fibonacci number, the sum of 8 and 13. That double membership is rare: apart from 1 and 3, the only Fibonacci numbers that are also triangular are 21 and 55, a fact proved in 1989. Twenty-one factors as 3 × 7, and it is the smallest number of distinct squares needed to tile a square, a puzzle first solved in 1978.
Nearby numbers
How to read this page
The factor list shows every way 21 splits into equal whole-number groups — 4 divisors in total. The prime factorisation is the compact form of that same information, and the base conversions restate 21 for contexts that do not use decimal.
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