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The number of divisors of 84 is 12. [6] As no smaller number has more than 12 divisors, 84 is a largely composite number. [7] The twenty-second unique prime in decimal, with notably different digits than its preceding (and known following) terms in the same sequence, contains a total of 84 digits. [8]
The tables below only list positive divisors. Key to the tables. d is the ... 84 40 deficient, composite 45: 1, 3, 5, 9, 15, 45 6 78 33 deficient, composite 46:
factors d(n) primorial ... 84 24 25200 4,2,2,1 9 ... A positive integer n is a largely composite number if d(n) ≥ d(m) for all m ≤ n.
If none of its prime factors are repeated, it is called squarefree. (All prime numbers and 1 are squarefree.) For example, 72 = 2 3 × 3 2, all the prime factors are repeated, so 72 is a powerful number. 42 = 2 × 3 × 7, none of the prime factors are repeated, so 42 is squarefree. Euler diagram of numbers under 100:
The entries in the table resolve this ambiguity by the following convention: the factors are primes in the right complex half plane with absolute value of the real part larger than or equal to the absolute value of the imaginary part. The entries are sorted according to increasing norm x 2 + y 2 (sequence A001481 in the OEIS). The table is ...
For positive integers a, gcd(a, a) = a. Every common divisor of a and b is a divisor of gcd(a, b). gcd(a, b), where a and b are not both zero, may be defined alternatively and equivalently as the smallest positive integer d which can be written in the form d = a⋅p + b⋅q, where p and q are integers.
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The multiplicity of a prime factor p of n is the largest exponent m for which p m divides n. The tables show the multiplicity for each prime factor. ... 84: 2 2 ·3 ...