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2. Karatsuba algorithm - Wikipedia

   en.wikipedia.org/wiki/Karatsuba_algorithm

   [1] [2] [3] It is a divide-and-conquer algorithm that reduces the multiplication of two n-digit numbers to three multiplications of n/2-digit numbers and, by repeating this reduction, to at most ⁡ single-digit multiplications.

3. Multiplication algorithm - Wikipedia

   en.wikipedia.org/wiki/Multiplication_algorithm

   More formally, multiplying two n-digit numbers using long multiplication requires Θ(n 2) single-digit operations (additions and multiplications). When implemented in software, long multiplication algorithms must deal with overflow during additions, which can be expensive.

4. Lattice multiplication - Wikipedia

   en.wikipedia.org/wiki/Lattice_multiplication

   If the sum contains more than one digit, the value of the tens place is carried into the next diagonal (see Step 2). Step 2. Numbers are filled to the left and to the bottom of the grid, and the answer is the numbers read off down (on the left) and across (on the bottom). In the example shown, the result of the multiplication of 58 with 213 is ...

5. Elementary arithmetic - Wikipedia

   en.wikipedia.org/wiki/Elementary_arithmetic

   The black numbers are the addends, the green number is the carry, and the blue number is the sum. In the rightmost digit, the addition of 9 and 7 is 16, carrying 1 into the next pair of the digit to the left, making its addition 1 + 5 + 2 = 8.

6. Grid method multiplication - Wikipedia

   en.wikipedia.org/wiki/Grid_method_multiplication

   The grid method (also known as the box method) of multiplication is an introductory approach to multi-digit multiplication calculations that involve numbers larger than ten. Because it is often taught in mathematics education at the level of primary school or elementary school , this algorithm is sometimes called the grammar school method.

7. Transposable integer - Wikipedia

   en.wikipedia.org/wiki/Transposable_integer

   When a parasitic number is multiplied by n, not only it exhibits the cyclic behavior but the permutation is such that the last digit of the parasitic number now becomes the first digit of the multiple. For example, 102564 x 4 = 410256. Note that 102564 is the repeating digits of 4 ⁄ 39 and 410256 the repeating digits of 16 ⁄ 39.