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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.
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 ).
where is the th successive prime number, and all omitted terms (a 22 to a 228) are factors with exponent equal to one (i.e. the number is ). More concisely, it is the product of seven distinct primorials:
He related α to the Eddington number, which was his estimate of the number of protons in the universe. [2] This led him in 1929 to conjecture that α was exactly 1/136. [3] He devised a "proof" that N Edd = 136 × 2 256, or about 1.57 × 10 79. Other physicists did not adopt this conjecture and did not accept his argument.
In number theory, a superior highly composite number is a natural number which, in a particular rigorous sense, has many divisors. Particularly, it is defined by a ratio between the number of divisors an integer has and that integer raised to some positive power.
The number of protons in the nucleus is the defining property of an element, and is referred to as the atomic number (represented by the symbol Z). Since each element is identified by the number of protons in its nucleus, each element has its own atomic number, which determines the number of atomic electrons and consequently the chemical ...
An example is calcium-40, with 20 neutrons and 20 protons, which is the heaviest stable isotope made of the same number of protons and neutrons. Both calcium-48 and nickel-48 are doubly magic because calcium-48 has 20 protons and 28 neutrons while nickel-48 has 28 protons and 20 neutrons. Calcium-48 is very neutron-rich for such a relatively ...
For other isotopes, the isotopic mass is usually within 0.1 u of the mass number. For example, 35 Cl (17 protons and 18 neutrons) has a mass number of 35 and an isotopic mass of 34.96885. [7] The difference of the actual isotopic mass minus the mass number of an atom is known as the mass excess, [8] which for 35 Cl is –0.03115.