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The multiplicity of a prime factor p of n is the largest exponent m for which p m ... A Ruth-Aaron pair is two consecutive numbers (x ... 76: 2 2 ·19 77: 7·11 78: 2 ...
76 is: a composite number; a square-prime, of the form (p 2, q) where q is a higher prime. It is the ninth of this general form and the seventh of the form (2 2.q). a Lucas number. [1] a telephone or involution number, the number of different ways of connecting 6 points with pairwise connections. [2] a nontotient. [3] a 14-gonal number. [4]
Two numbers with the same "abundancy" form a friendly pair; ... 76: 140: 35/19 77: 96: 96/77 ... at least one of the prime factors must be congruent to 1 modulo 3 and ...
The factorizations are often not unique in the sense that the unit could be absorbed into any other factor with exponent equal to one. The entry 4+2i = −i(1+i) 2 (2+i), for example, could also be written as 4+2i= (1+i) 2 (1−2i). The entries in the table resolve this ambiguity by the following convention: the factors are primes in the right ...
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:
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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.
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