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2. Divisibility rule - Wikipedia

   en.wikipedia.org/wiki/Divisibility_rule

   In fact, this rule for prime divisors besides 2 and 5 is really a rule for divisibility by any integer relatively prime to 10 (including 33 and 39; see the table below). This is why the last divisibility condition in the tables above and below for any number relatively prime to 10 has the same kind of form (add or subtract some multiple of the ...

3. Division (mathematics) - Wikipedia

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

   In terms of partition, 20 / 5 means the size of each of 5 parts into which a set of size 20 is divided. For example, 20 apples divide into five groups of four apples, meaning that "twenty divided by five is equal to four". This is denoted as 20 / 5 = 4, or ⁠ 20 / 5 ⁠ = 4. [2] In the example, 20 is the dividend, 5 is the divisor, and 4 is ...

4. Least common multiple - Wikipedia

   en.wikipedia.org/wiki/Least_common_multiple

   The least common multiple of the denominators of two fractions is the " lowest common denominator " (lcd), and can be used for adding, subtracting or comparing the fractions. The least common multiple of more than two integers a, b, c, . . . , usually denoted by lcm (a,b,c, . . .), is defined as the smallest positive integer that is divisible ...

5. Parity (mathematics) - Wikipedia

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

   Parity (mathematics) Cuisenaire rods: 5 (yellow) cannot be evenly divided in 2 (red) by any 2 rods of the same color/length, while 6 (dark green) can be evenly divided in 2 by 3 (lime green). In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is divisible by 2, and odd if it is not. [1]

6. Division by zero - Wikipedia

   en.wikipedia.org/wiki/Division_by_zero

   Following the ordinary rules of elementary algebra while allowing division by zero can create a mathematical fallacy, a subtle mistake leading to absurd results. To prevent this, the arithmetic of real numbers and more general numerical structures called fields leaves division by zero undefined , and situations where division by zero might ...

7. Euclid's lemma - Wikipedia

   en.wikipedia.org/wiki/Euclid's_lemma

   Euclid's lemma. In algebra and number theory, Euclid's lemma is a lemma that captures a fundamental property of prime numbers: [note 1] Euclid's lemma — If a prime p divides the product ab of two integers a and b, then p must divide at least one of those integers a or b. For example, if p = 19, a = 133, b = 143, then ab = 133 × 143 = 19019 ...