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  2. 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.

  3. Composite number - Wikipedia

    en.wikipedia.org/wiki/Composite_number

    If none of its prime factors are repeated, it is called squarefree. (All prime numbers and 1 are squarefree.) For example, 72 = 2 3 × 3 2, all the prime factors are repeated, so 72 is a powerful number. 42 = 2 × 3 × 7, none of the prime factors are repeated, so 42 is squarefree. Euler diagram of numbers under 100:

  4. Multiplication table - Wikipedia

    en.wikipedia.org/wiki/Multiplication_table

    In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system. The decimal multiplication table was traditionally taught as an essential part of elementary arithmetic around the world, as it lays the foundation for arithmetic operations ...

  5. Multiplication - Wikipedia

    en.wikipedia.org/wiki/Multiplication

    Multiplication by a positive number preserves the order: For a > 0, if b > c, then ab > ac. Multiplication by a negative number reverses the order: For a < 0, if b > c, then ab < ac. The complex numbers do not have an ordering that is compatible with both addition and multiplication. [30]

  6. Integer factorization - Wikipedia

    en.wikipedia.org/wiki/Integer_factorization

    Continuing this process until every factor is prime is called prime factorization; the result is always unique up to the order of the factors by the prime factorization theorem. To factorize a small integer n using mental or pen-and-paper arithmetic, the simplest method is trial division : checking if the number is divisible by prime numbers 2 ...

  7. Prime omega function - Wikipedia

    en.wikipedia.org/wiki/Prime_omega_function

    In number theory, the prime omega functions and () count the number of prime factors of a natural number . Thereby (little omega) counts each distinct prime factor, whereas the related function () (big omega) counts the total number of prime factors of , honoring their multiplicity (see arithmetic function).

  8. 63 (number) - Wikipedia

    en.wikipedia.org/wiki/63_(number)

    It is the only number in the Mersenne sequence whose prime factors are each factors of at least one previous element of the sequence (3 and 7, respectively the first and second Mersenne primes). [7] In the list of Mersenne numbers, 63 lies between Mersenne primes 31 and 127, with 127 the thirty-first prime number. [5]

  9. Coprime integers - Wikipedia

    en.wikipedia.org/wiki/Coprime_integers

    The resulting binary tree, the Calkin–Wilf tree, is exhaustive and non-redundant, which can be seen as follows. Given a coprime pair one recursively applies f − 1 {\displaystyle f^{-1}} or g − 1 {\displaystyle g^{-1}} depending on which of them yields a positive coprime pair with m > n .