1. All the whole and positive numbers that are part of the number system. Depending on the mathematical field, it can start at zero N = {0, 1, 2, 3, …} or 1 N = {1, 2, 3, 4, …} and, both cases, continue infinitely.

**Etymology**: Number, from Latin *numĕrus*with roots in Indo-European languages such as *nommer*conjugated on **nem-*, **name-*as to ‘assign’, ‘order’, and the suffix *-that*. + Natural, from Latin *naturalis*regarding *natum*for ‘born’, as participle of the verb *I will be born*for ‘born’, followed by the suffixes *-ūra*which attributes ‘quality’, and *-lis*as ‘associative mode’.

**Grammatical category**: masculine noun**in syllables**: na-tu-ral/-ra-les number/s.

## Natural numbers

**Evelyn Maitee Marin**

Industrial Engineer, MSc in Physics, and EdD

The natural numbers are a subset of the integers (and therefore of the real and complex numbers). This set includes those numbers that are used to count, that is, integer and positive values (most authors do not include zero). To every natural number there corresponds an immediate successor number.

*The number of students in a classroom is represented by a natural number.*

The set formed by the natural numbers is denoted with the symbol N, and is made up of infinite members, since the number of numbers that can be counted is endless:*N = { 1,2,3,4,5, … }*

Natural numbers are not only used for counting, since many mathematical operations can also be carried out with them, such as addition, subtraction, multiplication, division, potentiation and even other operators such as derivatives and integrals.

*The sum or product of two natural numbers results in another natural number.*

*The natural numbers are a subset of the integers.*

## Representation of natural numbers on the real line

The natural numbers are framed within a positional decimal numeral system, which implies that each digit within a number is associated with a value, in this way, when analyzing an eight-digit number (for example, 23,627,497), it is It is made up of 2 tens of a million, 3 units of a million, 6 hundred thousand, 2 tens of thousands, 7 units of a thousand, 4 hundreds, 9 tens and 7 units:

Now, if you want to represent a natural number on the number line, you must start by drawing a horizontal line and arbitrarily designate an origin where zero will be located (it is recommended to locate it at the extreme left).

The next step is to draw small vertical line segments equidistantly on the horizontal line, to represent each natural number. It must be taken into account that an appropriate separation between segments must be selected so that the quantity to be located on the line can be represented; For example, if the number to be located on the line is 5, it must be ensured that at least six segments fit on said line:

In the event that the amounts are very high, for example, 250. You can choose to use scales that allow the representation of said number. One option may be to consider that each division is equivalent to 50 units:

## Prime and Composite Numbers

The natural numbers can be decomposed and classified considering their divisors, so that there are natural numbers that can only be divided exactly between themselves and between the unit (1), and are known as prime numbers; and on the contrary, those that have more than two divisors, which are called composite numbers.

To identify if a quantity has more than two divisors, it is important to remember that the divisors allow, redundantly, the division of another number into exact parts, so in this kind of operation, the remainder is always zero. For example, it is known that the number 3 is a divisor of 18, since if we divide 18 by 3, the result is exactly 6, and the remainder or remainder of the division is zero.

It is very helpful when identifying the divisors of some numbers to know certain rules or basic divisibility criteria. Some of these rules are:

– Every even number is divisible by 2.

– Any number that ends in 5 or 0 is divisible by 5.

– Any number that ends in 0 is divisible by 10.

– If the sum of the digits of a number is a multiple of 3, then the whole number is divisible by 3.

With these considerations, it can be deduced that almost all the natural numbers from 1 to 100 are composite numbers, except the numbers shown in the following table:

## Example exercise with natural numbers

Students from 5 classrooms will meet on a school field. Each classroom has the following number of students:

Room A: 23 students

Room B: 17 students

Room C: 25 students

Room D: 20 students

Room E: 21 students

*How many students will meet on the court?*

To answer the question posed, simply add the number of students in each classroom. The number of people represents a natural number, therefore, the sum of the amounts of people will also be a natural number:

Number of students on the field = 23 + 17 + 25 + 20 + 21 = 106 students

Following