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Multiplication

Tool to make multiplication with large numbers (with lots of digits/figures). Standard calculators are limited with big numbers.

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Multiplication -

Tag(s) : Arithmetics

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# Multiplication

## Calculation with Multiplication

### How to calculate a multiplication with big numbers?

Multiplication is a basic arithmetic operation defined as the repetition of an addition.

Example: 3 times 2 $= 3 \times 2 = 2+2+2$

The dCode multiplication tool with big integers uses arbitrary precision calculation algorithms. That is to say that it is not limited to 4 billion and it can multiply exact values without rounding nor need of a scientific notation. It is called large/huge number multiplication.

### What are multiplication tables?

Traditionally multiplication tables refers to this table:

1 2 3 4 5 6 7 8 9 10 \ 1 2 3 4 5 6 7 8 9 10 2 4 6 8 10 12 14 16 18 20 3 6 9 12 15 18 21 24 27 30 4 8 12 16 20 24 28 32 36 40 5 10 15 20 25 30 35 40 45 50 6 12 18 24 30 36 42 48 54 60 7 14 21 28 35 42 49 56 63 70 8 16 24 32 40 48 56 64 72 80 9 18 27 36 45 54 63 72 81 90 10 20 30 40 50 60 70 80 90 100

### What is the Karatsuba algorithm?

In order to improve calculation time the multiplication is accelerated by decomposing it:

ab * cd = (a * 10^k + b) * (c * 10^k + d) = ac * 10^2k + (ad + bc) * 10^k + bd

This multiplication needs 4 values ac, ad, bc and bd. More:

(a * 10^k + b) * (c * 10^k + d) = ac * 10^2k + (ac + bd - (a - b)(c - d)) * 10^k + bd

The same multiplication needs 3 values: ac, bd and (a - b)(c - d).

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