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The tables below list all of the divisors of the numbers 1 to 1000. A divisor of an integer n is an integer m , for which n / m is again an integer (which is necessarily also a divisor of n ). For example, 3 is a divisor of 21, since 21/7 = 3 (and therefore 7 is also a divisor of 21).
Print/export Download as PDF ... Sphenic numbers always have exactly eight divisors. [6] 8 is the base of the octal number ... "8 (circle)" is the eighth song on the ...
In number theory, the aliquot sum s(n) of a positive integer n is the sum of all proper divisors of n, that is, all divisors of n other than n itself. That is, = |,. It can be used to characterize the prime numbers, perfect numbers, sociable numbers, deficient numbers, abundant numbers, and untouchable numbers, and to define the aliquot sequence of a number.
Abundancy may also be expressed as () where denotes a divisor function with () equal to the sum of the k-th powers of the divisors of n. The numbers 1 through 5 are all solitary. The smallest friendly number is 6, forming for example, the friendly pair 6 and 28 with abundancy σ(6) / 6 = (1+2+3+6) / 6 = 2, the same as σ(28) / 28 = (1+2+4+7+14 ...
For example, to find the Hall divisors of 60, its prime power factorization is 2 2 × 3 × 5, so one takes any product of 3, 2 2 = 4, and 5. Thus, the Hall divisors of 60 are 1, 3, 4, 5, 12, 15, 20, and 60. A Hall subgroup of G is a subgroup whose order is a Hall divisor of the order of G. In other words, it is a subgroup whose order is coprime ...
In number theory, Zsigmondy's theorem, named after Karl Zsigmondy, states that if > > are coprime integers, then for any integer , there is a prime number p (called a primitive prime divisor) that divides and does not divide for any positive integer <, with the following exceptions:
Adding up some subsets of its divisors (e.g., 6, 12, and 18) gives 36; hence, it is also the eighth semiperfect number. [ 7 ] This number is the sum of the cubes of the first three positive integers and also the product of the squares of the first three positive integers.
The divisors of n are all products of some or all prime factors of n (including the empty product 1 of no prime factors). The number of divisors can be computed by increasing all multiplicities by 1 and then multiplying them. Divisors and properties related to divisors are shown in table of divisors.