Twenty-eight is the integer that follows 27 and precedes 29. It is an even whole number often encountered in counting, measurement and everyday contexts. As a composite number it has a small set of exact divisors and several notable mathematical identities.
Mathematical properties
Its positive divisors are:
- 1, 2, 4, 7, 14, 28
Excluding the number itself, the proper divisors 1 + 2 + 4 + 7 + 14 sum to 28. Because its proper divisors add up to the number, 28 is classified as a perfect number. The previous perfect number in the sequence is six.
Further numerical features
Twenty-eight appears in several elementary formulas and representations: it is the 7th triangular number (7·8/2 = 28), also a hexagonal number, and equals the binomial coefficient C(8,2). In base representations it is 11100 in binary and 1C in hexadecimal. The even perfect numbers correspond to the formula 2^(p-1)·(2^p−1) when 2^p−1 is prime; for p = 3 this yields 28.
Occurrences and uses
Outside pure mathematics, 28 is the atomic number of nickel, an element used widely in alloys and plating. The Gregorian calendar commonly associates 28 with February in non-leap years (February has 28 days). Cultural and biological references (for example, average cycle lengths) vary and should be treated as approximate rather than fixed facts.
Notable distinctions
As the second perfect number and a small composite with few divisors, 28 serves as a standard example in elementary number theory and recreational mathematics. Its combination of combinatorial, polygonal and divisor properties makes it a frequent illustration in textbooks and problem collections. For further reading about basic integers and classification, see general resources on numbers and divisibility: divisibility and factors.
If you need more technical details or proofs about perfect numbers, triangular numbers or the Mersenne-prime connection, consult introductory number-theory material or reference summaries online and in textbooks: number overview.