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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.
This fact can be used to find the lcm of a set of numbers. Example: lcm(8,9,21) Factor each number and express it as a product of prime number powers. = = = The lcm will be the product of multiplying the highest power of each prime number together. The highest power of the three prime numbers 2, 3, and 7 is 2 3, 3 2, and 7 1, respectively. Thus,
The number of steps to calculate the GCD of two natural numbers, a and b, may be denoted by T(a, b). [96] If g is the GCD of a and b, then a = mg and b = ng for two coprime numbers m and n. Then T(a, b) = T(m, n) as may be seen by dividing all the steps in the Euclidean algorithm by g. [97]
There usually are fewer 2-digit Friedman numbers than 3-digit and more in any given base, but the 2-digit ones are easier to find. If we represent a 2-digit number as mb + n, where b is the base and m, n are integers from 0 to b−1, we need only check each possible combination of m and n against the equalities mb + n = m n, and mb + n = n m to see which ones are true.
An economical number has been defined as a frugal number, but also as a number that is either frugal or equidigital. gcd( m , n ) ( greatest common divisor of m and n ) is the product of all prime factors which are both in m and n (with the smallest multiplicity for m and n ).
the k given prime numbers p i must be precisely the first k prime numbers (2, 3, 5, ...); if not, we could replace one of the given primes by a smaller prime, and thus obtain a smaller number than n with the same number of divisors (for instance 10 = 2 × 5 may be replaced with 6 = 2 × 3; both have four divisors);
The Motorola 6800 microprocessor was the first for which an undocumented assembly mnemonic HCF became widely known. The operation codes (opcodes—the portions of the machine language instructions that specify an operation to be performed) hexadecimal 9D and DD were reported and given the unofficial mnemonic HCF in a December 1977 article by Gerry Wheeler in BYTE magazine on undocumented ...
The output of each was sent to its own looped wire, or as they are referred to in this system, a "field coil". Two such coils, one for each antenna, are arranged close together at right angles. The signals from the two antennas generated a magnetic field in the space between the coils, which was picked up by a rotating solenoid, the "search ...