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  2. Greatest common divisor - Wikipedia

    en.wikipedia.org/wiki/Greatest_common_divisor

    The elements 2 and 1 + √ −3 are two maximal common divisors (that is, any common divisor which is a multiple of 2 is associated to 2, the same holds for 1 + √ −3, but they are not associated, so there is no greatest common divisor of a and b.

  3. Least common multiple - Wikipedia

    en.wikipedia.org/wiki/Least_common_multiple

    A multiple of a number is the product of that number and an integer. For example, 10 is a multiple of 5 because 5 × 2 = 10, so 10 is divisible by 5 and 2. Because 10 is the smallest positive integer that is divisible by both 5 and 2, it is the least common multiple of 5 and 2.

  4. Table of prime factors - Wikipedia

    en.wikipedia.org/wiki/Table_of_prime_factors

    lcm(m, n) (least common multiple of m and n) is the product of all prime factors of m or n (with the largest multiplicity for m or n). gcd(m, n) × lcm(m, n) = m × n. Finding the prime factors is often harder than computing gcd and lcm using other algorithms which do not require known prime factorization. m is a divisor of n (also called m ...

  5. Glossary of number theory - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_number_theory

    Bézout's identity Bézout's identity, also called Bézout's lemma, states that if d is the greatest common divisor of two integers a and b, then there exists integers x and y such that ax + by = d, and in fact the integers of the form as + bt are exactly the multiples of d.

  6. Fundamental theorem of arithmetic - Wikipedia

    en.wikipedia.org/wiki/Fundamental_theorem_of...

    Factors p 0 = 1 may be inserted without changing the value of n (for example, 1000 = 2 3 ×3 0 ×5 3). In fact, any positive integer can be uniquely represented as an infinite product taken over all the positive prime numbers, as

  7. Highly composite number - Wikipedia

    en.wikipedia.org/wiki/Highly_composite_number

    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:

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