How To Multiply Large Numbers Quickly

The concept of multiplication in mathematics

How To Multiply Large Numbers Quickly

About a thousand years ago, the Babylonians invented the method of multiplication in mathematics, and after that there were many methods of multiplication until scientists reached the optimal way to multiply numbers in mathematics used in our time. Relatively, for example, if you want to multiply two numbers of two digits each, you will need to perform four smaller multiplications, This method is called the convection method, and the number of smaller multiplications in this method is n² as n; It is the number of digits for each number of the numbers you multiply, so if you want to multiply two numbers,

each of which consists of 3 digits, you will need nine smaller multiplications, and therefore this method will not work if the multiplied numbers are large, for example if you want to multiply two numbers each If you want to multiply two numbers, each of them consists of A billion digits using the pregnancy method, the latest computers will need 30 years to solve it by following the pregnancy method, so the process of carrying is suitable for small numbers and not suitable for large numbers.

How to multiply large numbers

There are many ways in which the product of multiplying large numbers can be calculated, the most important of which are:

Karatsuba method

The Karatsuba method involves dismantling the numbers and then regrouping them in a way that allows more time for the multiplication process. To calculate the result of multiplying the numbers 25 and 36 using the Karatsuba method, follow these steps:
  • Divide the number 25 into two digits, 5 and 2.
  • Divide 63 into two digits, 3 and 6.
  • Multiply the number 2 by the number 6, and the result is 12.
  • Multiply the number 5 by the number 3, and the result is 15.
  • Combine the two parts of the number 25, which are the numbers 5 and 2, and their sum = 7.
  • Combine the two parts that make up the number 63, which are the numbers 3 and 6, and their sum = 9. Multiply the product of the two parts of the first number by the sum of the two parts of the second number = 7 * 9 = 63.
  • Now subtract the two numbers obtained from the third and fourth steps from the number obtained from the seventh step = 63-15-12 = 36.
  • Take the resulting number from the third step and put it to the right of it Two zeros to become 1200.
  • Take the number obtained from step eight and put a zero to the right of it to become 360.
  • Add the resulting number from the ninth step with the resulting number from the tenth step with the resulting number from the fourth step = 1200 + 360 + 15 = 1575. Therefore, the product of multiplying the numbers 25 and 36 is 1575.

Multiply large numbers using abbreviations


The method of calculating the result of multiplying large numbers can be understood through this method through the following example. To calculate the result of multiplying the numbers 12 and 325 using the abbreviation method, follow these steps:
  • Divide the number 12 into two numbers whose sum is 2 and 10, and it is preferable to choose numbers that are multiples of ten in such cases.
  • Multiply the number 325 by the number 10 and the result = 3250.
  • Multiply the number 325 by the number 2 and the result is = 650.
  • Add the resulting number from the first operation with the number obtained from the second operation = 3250 + 650 = 3900, so the result of multiplying the numbers 12 and 325 is 3900.

Quick tricks to multiply numbers

There are many tricks that enable you to multiply numbers in a faster and easier way, the most famous of which are:

How to multiply any integer number by multiples of 10

Any integer number can be multiplied by multiples of ten in a quick way, as we put the number of zeros in the number that represents the multiple of 10 on the right, and we put the numbers we want to multiply to the left of these zeros, as the result of multiplying the number 678 by the number 100 by following these steps:
  1. Put the number of zeros in 100 or its multiples, which here are two zeros to the right.
  2. Put the numbers on 678 to the left of the zero and the result is = 67800.
  3. Also, if we multiply the number 5 by the number 10, the result is 50.

Easy way to multiply numbers from 11-19

To multiply the numbers from 11-19, we take the ones digit from each number, and then multiply them together the first time and put the result in the ones place, then add them together and put the result in the tens place, then put the number one in the hundreds place, and the following are some examples that clarify That process:
  1. Example (1): 11 x 13 = 1 x 3 = 3, which we put in the ones place, 1 + 3 = 4, which we put in the tens place, and then we put the number one in the hundreds place, so the result is 143.
  2. Example (2) : 12 x 14 = 2 x 4 = 8, which we put in the ones place, 2 + 4 = 6, which we put in the tens place, and then we put the number one in the hundreds place, so the result is 168.
  3. Example (3): 13 x 13 = 3 x 3 = 9, which we put in the ones place, 3 + 3 = 6, which we put in the tens place, and then we put the number one in the hundreds place, so the result is 169.
The product of multiplying or adding the ones of the two multiplied numbers may be greater than 10, and the solution is to raise the tens number by hand, just as we deal with normal addition, and the following are examples of that:
  • Example (1): 19 x 14 = 9 x 4 = 36 (we put the number six in the units of the product, and the number three is set aside), 9 + 4 = 13 (we put the number three in the tens after adding the previous three to it, and then add the number One to the number one, which we basically put in the hundreds place), so the result is 266.
  • Example (2): 13 x 15 = 3 x 5 = 15 (we put the number five in the units of the product, and one is put aside), 3 + 5 = 8 (add to the number 8 (the one set aside), and then we add the number one to the hundreds place, so 195.

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