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If one uses the Euclidean algorithm and the elementary algorithms for multiplication and division, the computation of the greatest common divisor of two integers of at most n bits is O(n 2). This means that the computation of greatest common divisor has, up to a constant factor, the same complexity as the multiplication.
For example, 3 is a divisor of 21, since 21/7 = 3 (and therefore 7 is also a divisor of 21). If m is a divisor of n , then so is − m . The tables below only list positive divisors.
Many properties of a natural number n can be seen or directly computed from the prime factorization of n.. The multiplicity of a prime factor p of n is the largest exponent m for which p m divides n.
1, 2, 3, 211, 5, 23, 7, 3331113965338635107, 311, 773, ... For n ≥ 2, a ( n ) is the prime that is finally reached when you start with n , concatenate its prime factors (A037276) and repeat until a prime is reached; a ( n ) = −1 if no prime is ever reached.
Synonyms for GCD include greatest common factor (GCF), highest common factor (HCF), highest common divisor (HCD), and greatest common measure (GCM). The greatest common divisor is often written as gcd( a , b ) or, more simply, as ( a , b ) , [ 3 ] although the latter notation is ambiguous, also used for concepts such as an ideal in the ring of ...
The Erdős–Woods numbers can be characterized in terms of certain partitions of the prime numbers.A number k is an Erdős–Woods number if and only if the prime numbers less than k can be partitioned into two subsets X and Y with the following property: for every pair of positive integers x and y with x + y = k, either x is divisible by a prime in X, or y is divisible by a prime in Y.
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
Since the greatest prime factor of + = is 157, which is more than 28 twice, 28 is a Størmer number. [ 3 ] Twenty-eight is a harmonic divisor number , [ 4 ] a happy number , [ 5 ] the 7th triangular number , [ 6 ] a hexagonal number , [ 7 ] a Leyland number of the second kind [ 8 ] ( 2 6 − 6 2 {\displaystyle 2^{6}-6^{2}} ), and a centered ...