84 (number)
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84 is a natural number that comes after 83 and before 85. It is a composite number that can be formed by multiplying smaller prime numbers, and is a commonly occurring number in mathematics and everyday life, particularly in counting time periods and dividing groups.
The Roman numeral for 84 is LXXXIV. In binary it is written as 1010100, while in hexadecimal it is 54.
Mathematical properties
The prime factorization of 84 is 2² × 3 × 7. It has twelve divisors: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84. The sum of its proper divisors is 140, which exceeds 84 itself—for this reason 84 is classified as an abundant number.
84 is a tetrahedral number, which is the sum of the first seven triangular numbers: 7 × 8 × 9 ÷ 6 = 84. It also equals the number of ways to choose three items from nine items (C(9,3) = 84).
84 is the sum of two twin primes that cannot be divided evenly: 41 + 43. It also equals 12 × 7, making it suitable for dividing groups of twelve or seven.
Other uses
84 appears in counting years (for example, the year 84 in historical records), counting months (84 months = seven years), and in numbering systems used in games and communications. It is also used as an identification number by various different organizations.