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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 ...
The First 48, an American crime program, 2004-present. 48 Hours is a television news program on CBS. 48 Hrs., a 1982 film starring Nick Nolte and Eddie Murphy, followed by Another 48 Hrs. Arizona is the 48th state in the United States. The 48 United States (excluding Alaska and Hawaii) are also referred to as the "Lower 48" or the "48 ...
The first few pairs of betrothed numbers (sequence A005276 in the OEIS) are: (48, 75), (140, 195), (1050, 1925), (1575, 1648), (2024, 2295), (5775, 6128). All known pairs of betrothed numbers have opposite parity. Any pair of the same parity must exceed 10 10.
Greatest common divisors can be computed by determining the prime factorizations of the two numbers and comparing factors. For example, to compute gcd(48, 180), we find the prime factorizations 48 = 2 4 · 3 1 and 180 = 2 2 · 3 2 · 5 1; the GCD is then 2 min(4,2) · 3 min(1,2) · 5 min(0,1) = 2 2 · 3 1 · 5 0 = 12 The corresponding LCM is ...
All pairs of positive coprime numbers (m, n) (with m > n) can be arranged in two disjoint complete ternary trees, one tree starting from (2, 1) (for even–odd and odd–even pairs), [10] and the other tree starting from (3, 1) (for odd–odd pairs). [11] The children of each vertex (m, n) are generated as follows:
d() is the number of positive divisors of n, including 1 and n itself; σ() is the sum of the positive divisors of n, including 1 and n itselfs() is the sum of the proper divisors of n, including 1 but not n itself; that is, s(n) = σ(n) − n
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The same method can also be illustrated with a Venn diagram as follows, with the prime factorization of each of the two numbers demonstrated in each circle and all factors they share in common in the intersection. The lcm then can be found by multiplying all of the prime numbers in the diagram. Here is an example: 48 = 2 × 2 × 2 × 2 × 3,