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  2. Table of prime factors - Wikipedia

    en.wikipedia.org/wiki/Table_of_prime_factors

    m is a divisor of n (also called m divides n, or n is divisible by m) if all prime factors of m have at least the same multiplicity in n. The divisors of n are all products of some or all prime factors of n (including the empty product 1 of no prime factors). The number of divisors can be computed by increasing all multiplicities by 1 and then ...

  3. Friendly number - Wikipedia

    en.wikipedia.org/wiki/Friendly_number

    For example, the "primitive" friendly pair 6 and 28 gives rise to friendly pairs 6n and 28n for all n that are congruent to 1, 5, 11, 13, 17, 19, 23, 25, 29, 31, 37, or 41 modulo 42. [4] This shows that the natural density of the friendly numbers (if it exists) is positive.

  4. 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:

  5. Pythagorean triple - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_triple

    More generally, a positive integer c is the hypotenuse of a primitive Pythagorean triple if and only if each prime factor of c is congruent to 1 modulo 4; that is, each prime factor has the form 4n + 1. In this case, the number of primitive Pythagorean triples (a, b, c) with a < b is 2 k−1, where k is the number of distinct prime factors of c ...

  6. Least common multiple - Wikipedia

    en.wikipedia.org/wiki/Least_common_multiple

    where the denominator 42 was used, because it is the least common multiple of 21 and 6. ... Factor each number and express it as a product of ... The following pairs ...

  7. Integer factorization - Wikipedia

    en.wikipedia.org/wiki/Integer_factorization

    If one of the factors is composite, it can in turn be written as a product of smaller factors, for example 60 = 3 · 20 = 3 · (5 · 4). 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.

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  9. Amicable numbers - Wikipedia

    en.wikipedia.org/wiki/Amicable_numbers

    However, amicable numbers where the two members have different smallest prime factors do exist: there are seven such pairs known. [8] Also, every known pair shares at least one common prime factor. It is not known whether a pair of coprime amicable numbers exists, though if any does, the product of the two must be greater than 10 65.