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  2. Divisibility rule - Wikipedia

    en.wikipedia.org/wiki/Divisibility_rule

    Another method is multiplication by 3. A number of the form 10x + y has the same remainder when divided by 7 as 3x + y. One must multiply the leftmost digit of the original number by 3, add the next digit, take the remainder when divided by 7, and continue from the beginning: multiply by 3, add the next digit, etc.

  3. Chinese remainder theorem - Wikipedia

    en.wikipedia.org/wiki/Chinese_remainder_theorem

    If one knows that the remainder of n divided by 3 is 2, the remainder of n divided by 5 is 3, and the remainder of n divided by 7 is 2, then with no other information, one can determine the remainder of n divided by 105 (the product of 3, 5, and 7) without knowing the value of n. In this example, the remainder is 23.

  4. Euclidean algorithm - Wikipedia

    en.wikipedia.org/wiki/Euclidean_algorithm

    A 24×60 rectangular area can be divided into a grid of 12×12 squares, with two squares along one edge (24/12 = 2) and five squares along the other (60/12 = 5). The greatest common divisor of two numbers a and b is the product of the prime factors shared by the two numbers, where each prime factor can be repeated as many times as it divides ...

  5. Euclidean division - Wikipedia

    en.wikipedia.org/wiki/Euclidean_division

    17 is divided into 3 groups of 5, with 2 as leftover. Here, the dividend is 17, the divisor is 3, the quotient is 5, and the remainder is 2 (which is strictly smaller than the divisor 3), or more symbolically, 17 = (3 × 5) + 2.

  6. Long division - Wikipedia

    en.wikipedia.org/wiki/Long_division

    Decimal numbers are not divided directly, the dividend and divisor are multiplied by a power of ten so that the division involves two whole numbers. Therefore, if one were dividing 12,7 by 0,4 (commas being used instead of decimal points), the dividend and divisor would first be changed to 127 and 4, and then the division would proceed as above.

  7. Polynomial remainder theorem - Wikipedia

    en.wikipedia.org/wiki/Polynomial_remainder_theorem

    Thus, the function may be more "cheaply" evaluated using synthetic division and the polynomial remainder theorem. The factor theorem is another application of the remainder theorem: if the remainder is zero, then the linear divisor is a factor. Repeated application of the factor theorem may be used to factorize the polynomial. [3]

  8. Division by zero - Wikipedia

    en.wikipedia.org/wiki/Division_by_zero

    Zero divided by a negative or positive number is either zero or is expressed as a fraction with zero as numerator and the finite quantity as denominator. Zero divided by zero is zero. In 830, Mahāvīra unsuccessfully tried to correct the mistake Brahmagupta made in his book Ganita Sara Samgraha: "A number remains unchanged when divided by zero ...

  9. Quater-imaginary base - Wikipedia

    en.wikipedia.org/wiki/Quater-imaginary_base

    Because d 0 − 4 d 2 + 16 d 4 = 7 and because—by the nature of the quater-imaginary system—the coefficients can only be 0, 1, 2 or 3 the value of the coefficients can be found. A possible configuration could be: d 0 = 3, d 2 = 3 and d 4 = 1. This configuration gives the resulting digit string for 7 10.