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  2. Divisibility rule - Wikipedia

    en.wikipedia.org/wiki/Divisibility_rule

    Pohlman–Mass method of divisibility by 7 The Pohlman–Mass method provides a quick solution that can determine if most integers are divisible by seven in three steps or less. This method could be useful in a mathematics competition such as MATHCOUNTS, where time is a factor to determine the solution without a calculator in the Sprint Round.

  3. Divisor - Wikipedia

    en.wikipedia.org/wiki/Divisor

    In definitions that allow the divisor to be 0, the relation of divisibility turns the set of non-negative integers into a partially ordered set that is a complete distributive lattice. The largest element of this lattice is 0 and the smallest is 1.

  4. Least common multiple - Wikipedia

    en.wikipedia.org/wiki/Least_common_multiple

    The positive integers may be partially ordered by divisibility: if a divides b (that is, if b is an integer multiple of a) write a ≤ b (or equivalently, b ≥ a). (Note that the usual magnitude-based definition of ≤ is not used here.) Under this ordering, the positive integers become a lattice, with meet given by the gcd and join given by ...

  5. Division (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Division_(mathematics)

    The simplest way of viewing division is in terms of quotition and partition: from the quotition perspective, 20 / 5 means the number of 5s that must be added to get 20. In terms of partition, 20 / 5 means the size of each of 5 parts into which a set of size 20 is divided.

  6. Glossary of mathematical symbols - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_mathematical...

    Many different uses in mathematics; see Asterisk § Mathematics. | 1. Divisibility: if m and n are two integers, means that m divides n evenly. 2. In set-builder notation, it is used as a separator meaning "such that"; see { | }. 3.

  7. Partially ordered set - Wikipedia

    en.wikipedia.org/wiki/Partially_ordered_set

    Fig. 3 Graph of the divisibility of numbers from 1 to 4. This set is partially, but not totally, ordered because there is a relationship from 1 to every other number, but there is no relationship from 2 to 3 or 3 to 4. Standard examples of posets arising in mathematics include:

  8. Parity (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Parity_(mathematics)

    The following laws can be verified using the properties of divisibility. They are a special case of rules in modular arithmetic, and are commonly used to check if an equality is likely to be correct by testing the parity of each side. As with ordinary arithmetic, multiplication and addition are commutative and associative in modulo 2 arithmetic ...

  9. Divisibility (ring theory) - Wikipedia

    en.wikipedia.org/wiki/Divisibility_(ring_theory)

    Divisibility is a useful concept for the analysis of the structure of commutative rings because of its relationship with the ideal structure of such rings. Definition [ edit ]