Search results
Results from the WOW.Com Content Network
m is a divisor of n (also called m divides n, or n is divisible by m) if all prime factors of m have at least the same multiplicity in n. 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 ...
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 greatest common divisor (GCD) of integers a and b, at least one of which is nonzero, is the greatest positive integer d such that d is a divisor of both a and b; that is, there are integers e and f such that a = de and b = df, and d is the largest such integer.
If one of the factors is composite, it can in turn be written as a product of smaller factors, for example 60 = 3 · 20 = 3 · (5 · 4). Continuing this process until every factor is prime is called prime factorization; the result is always unique up to the order of the factors by the prime factorization theorem.
If the Euclidean algorithm requires N steps for a pair of natural numbers a > b > 0, the smallest values of a and b for which this is true are the Fibonacci numbers F N+2 and F N+1, respectively. [98] More precisely, if the Euclidean algorithm requires N steps for the pair a > b, then one has a ≥ F N+2 and b ≥ F N+1.
The polynomial x 2 + cx + d, where a + b = c and ab = d, can be factorized into (x + a)(x + b).. In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.
Prime factors of the base: 2, 5 Prime factors of one below the base: 3 Prime factors of one above the base: 11 Other prime factors: 7 13 17 19 23 29 31: Quaternary base Prime factors of the base: 2 Prime factors of one below the base: 3 Prime factors of one above the base: 5 (=11 4) Other prime factors: 13 23 31 101 103 113 131 133: Fraction ...
The ρ algorithm was a good choice for F 8 because the prime factor p = 1238926361552897 is much smaller than the other factor. The factorization took 2 hours on a UNIVAC 1100/42 . [ 4 ]