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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 ...
54 as the sum of three positive squares. 54 is an abundant number [1] because the sum of its proper divisors (), [2] which excludes 54 as a divisor, is greater than itself. Like all multiples of 6, [3] 54 is equal to some of its proper divisors summed together, [a] so it is also a semiperfect number. [4]
This article gives a list of conversion factors for several physical quantities. A number of different units (some only of historical interest) ... = 2.54 × 10 −5 ...
Denoting this remainder as a mod b, the algorithm replaces (a, b) with (b, a mod b) repeatedly until the pair is (d, 0), where d is the greatest common divisor. For example, to compute gcd(48,18), the computation is as follows:
If all e i ≡ 1 (mod 3) or 2 (mod 5), then the smallest prime factor of N must lie between 10 8 and 10 1000. [41] More generally, if all 2e i +1 have a prime factor in a given finite set S, then the smallest prime factor of N must be smaller than an effectively computable constant depending only on S. [41]
However, amicable numbers where the two members have different smallest prime factors do exist: there are seven such pairs known. [8] Also, every known pair shares at least one common prime factor. It is not known whether a pair of coprime amicable numbers exists, though if any does, the product of the two must be greater than 10 65.
Choose your favorite pair, and don't forget to tag your own partner or sidekick. #1 Tom and Jerry Tom and Jerry are the ultimate cat-and-mouse duo, amusing us with their endless game of chase.
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.