We explain what natural numbers are and some of their characteristics. The greatest common divisor and the least common multiple.

## What are natural numbers?

The natural numbers are** the numbers that in the history of man first served to count objects** not only for accounting but also for ordering 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 see, these numbers do not allow fractions (decimals). It should be clarified that** the number zero Sometimes it is considered a natural number** but generally this is not the case.

On the other hand, it is said that natural numbers always have a successor number and the natural numbers ** do not discriminate between numbers peers and odd** they understand all of them. They do not allow fractions or negative numbers. They are distinguished from integers, since integers also include negative numbers. Regarding the written expression of natural numbers, these are represented with the letter N, in capital letters.

The 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 basic elements without which mathematics could not occur, also all sciences that use this type of calculations such as geometry, engineering, chemistry, physics, all require mathematics and natural numbers.

**The greatest common factor**It is the largest natural number that has the mathematical ability to divide each of the given numbers. To find this number it is necessary to first decompose the number into prime numbers, choosing only common factors with the lowest exponent and calculating the product of the factors.**The Least Common Multiple**It is the smallest natural number multiple of each of the given numbers in a particular distribution. And your steps to find it are to decompose the number into prime numbers, choose prime factors with the highest exponent and then calculate the product of said factors.

Mainly two uses are distinguished that are fundamental, firstly **to describe the position occupied by a given element within an ordered sequence** and to specify the size of a finite set, which in turn generalizes into the concept of cardinal number (set theory). And secondly, the other very important use is that of the mathematical construction of integers.

**The order of the natural numbers in a given operation does not alter the result** this is the so-called “commutative property” of natural numbers.