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Instead, the division is reduced to small steps. Starting from the left, enough digits are selected to form a number (called the partial dividend) that is at least 4×1 but smaller than 4×10 (4 being the divisor in this problem). Here, the partial dividend is 9. The first number to be divided by the divisor (4) is the partial dividend (9).
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
In these examples, the (negative) least absolute remainder is obtained from the least positive remainder by subtracting 5, which is d. This holds in general. When dividing by d, either both remainders are positive and therefore equal, or they have opposite signs. If the positive remainder is r 1, and the negative one is r 2, then r 1 = r 2 + d.
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 ...
This first statement was restricted to the following example: 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 ...
An example of a decision problem is deciding with the help of an algorithm whether a given natural number is prime. Another example is the problem, "given two numbers x and y, does x evenly divide y?" A method for solving a decision problem, given in the form of an algorithm, is called a decision procedure for that problem.
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