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Animation showing an application of the Euclidean algorithm to find the greatest common divisor of 62 and 36, which is 2. A more efficient method is the Euclidean algorithm , a variant in which the difference of the two numbers a and b is replaced by the remainder of the Euclidean division (also called division with remainder ) of a by b .
Download as PDF; Printable version; ... a superior highly composite number has a ratio between its number of divisors and itself raised ... 18, 27, 36, 54, 81, 108 ...
A refactorable number or tau number is an integer n that is divisible by the count of its divisors, or to put it algebraically, n is such that (). The first few refactorable numbers are listed in (sequence A033950 in the OEIS ) as
In this case, the greatest common divisor of 2u and u 2 + 3v 2 is 3. That implies that 3 divides u, and one may express u = 3w in terms of a smaller integer, w. Since u is divisible by 4, so is w; hence, w is also even. Since u and v are coprime, so are v and w. Therefore, neither 3 nor 4 divide v. Substituting u by w in the equation for z 3 yields
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
gcd – greatest common divisor of two numbers. (Also written as hcf.) gd – Gudermannian function. GF – Galois field. GF – generating function. GL – general linear group. G.M. – geometric mean. glb – greatest lower bound. (Also written as inf.) G.P. – geometric progression. grad – gradient of a function.
The Euclidean algorithm is based on the principle that the greatest common divisor of two numbers does not change if the larger number is replaced by its difference with the smaller number. For example, 21 is the GCD of 252 and 105 (as 252 = 21 × 12 and 105 = 21 × 5) , and the same number 21 is also the GCD of 105 and 252 − 105 = 147 .
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 ).