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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.
For example, addition and division, the factorial and exponential function, and the function which returns the nth prime are all primitive recursive. [1] In fact, for showing that a computable function is primitive recursive, it suffices to show that its time complexity is bounded above by a primitive recursive function of the input size. [2]
In the next step, b(x) is divided by r 0 (x) yielding a remainder r 1 (x) = x 2 + x + 2. Finally, dividing r 0 (x) by r 1 (x) yields a zero remainder, indicating that r 1 (x) is the greatest common divisor polynomial of a(x) and b(x), consistent with their factorization. Many of the applications described above for integers carry over to ...
In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor. [1]
In arithmetic, Euclidean division – or division with remainder – is the process of dividing one integer (the dividend) by another (the divisor), in a way that produces an integer quotient and a natural number remainder strictly smaller than the absolute value of the divisor. A fundamental property is that the quotient and the remainder ...
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Lightly spray an 8x8 pan with cooking spray or line with parchment paper. Crumble about 2/3 of the cookie dough into the pan and press into an even layer, like a crust.
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. For example, the number 371: 3×3 + 7 = 16 remainder 2, and 2×3 + 1 = 7. This method can be used to find the remainder of division by 7.