What are natural numbers?
Natural numbers are the numbers that, in the history of man, were first used to count objects for accounting and order them. These numbers start from the number 1. There is no total or final amount of natural numbers; they are infinite.
The natural numbers are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10… etc. As we can see, these numbers do not admit fractions (decimals). It should be noted that the number zero is sometimes considered a natural number, but generally, it is not.
On the other hand, natural numbers always have a successor number. And raw numbers do not discriminate between even and odd numbers; they include all of them. They do not accept fractions or negative numbers. They are distinguished from integers since integers also have negative numbers. As for the written expression of the natural numbers, these are represented by the letter N in capital letters.
Natural numbers are also the primary basis on which all mathematical operations and functions are based, addition, subtraction, multiplication, and division. Also, to trigonometric functions and equations. In short, they are the essential elements without which mathematics could not occur. Also, all the sciences that use this type of calculation, such as geometry, engineering, chemistry, and physics, require mathematics and natural numbers.
Classification of natural numbers.
The Greatest Common Factor. It is the most significant natural number with the mathematical ability to divide the given numbers. To find this number, it is necessary first to decompose the number into prime numbers, choose only common factors with the lowest exponent, and calculate the product of the elements.
The Least Common Multiple. It is the smallest natural number multiple of the given numbers in a particular distribution. And the steps to find it are decomposing the number into prime numbers, choosing the prime factors with the most prominent exponent, and then calculating the product of those factors.
Mainly two uses are fundamental: first, to describe the position occupied by a specific element within an ordered sequence and to specify the size of a finite set, which s generalized in the concept of cardinal number ( set theory). And secondly, the other use of great importance is the mathematical construction of integers.
The order of the natural numbers in a given operation does not alter the result; this is the “commutative property” of the natural numbers.