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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. Fundamental theorem of arithmetic - Wikipedia

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

    As the positive integers less than s have been supposed to have a unique prime factorization, must occur in the factorization of either or Q. The latter case is impossible, as Q , being smaller than s , must have a unique prime factorization, and p 1 {\displaystyle p_{1}} differs from every q j . {\displaystyle q_{j}.}

  4. 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 ...

  5. List of number theory topics - Wikipedia

    en.wikipedia.org/wiki/List_of_number_theory_topics

    Prime number, prime power. Bonse's inequality; Prime factor. Table of prime factors; Formula for primes; Factorization. RSA number; Fundamental theorem of arithmetic; Square-free. Square-free integer; Square-free polynomial; Square number; Power of two; Integer-valued polynomial

  6. Prime number - Wikipedia

    en.wikipedia.org/wiki/Prime_number

    The same prime factor may occur more than once; this example has two copies of the prime factor When a prime occurs multiple times, exponentiation can be used to group together multiple copies of the same prime number: for example, in the second way of writing the product above, 5 2 {\displaystyle 5^{2}} denotes the square or second power of 5 ...

  7. Fermat's factorization method - Wikipedia

    en.wikipedia.org/wiki/Fermat's_factorization_method

    Fermat's factorization method, named after Pierre de Fermat, is based on the representation of an odd integer as the difference of two squares: N = a 2 − b 2 . {\displaystyle N=a^{2}-b^{2}.} That difference is algebraically factorable as ( a + b ) ( a − b ) {\displaystyle (a+b)(a-b)} ; if neither factor equals one, it is a proper ...

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