NATURAL NUMBERS
Natural Numbers
A natural number is a number that occurs commonly and obviously in nature. As such, it is a whole, non-negative number. Natural numbers are also called Whole numbers or Counting numbers. The symbols 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 constitute the natural numbers and are used for counting.
Decimal System
The word "Decimal" really means "based on 10" (From Latin decima: a tenth part). This is based on the ten symbols we are familiar with.
Take a look at the number ‘14’.
In this number, the left digit ‘1’ is called the ‘ones digit’ and the right digit ‘4’ is the tens digit. Together, they are called Fourteen as this a number between 10 and 99, it ends with the tens digit.
Once a number enters the 3 digit criteria, it enters the hundreds digit.
Take a look at the number ‘111’.
Here, the left digit ‘1’ is the ones digit. The second left digit ‘1’is a tens digit and the third and last digit ‘1’ is the hundreds digit.
In a number containing more than 2 digits, as we go from left to right, the first, second and the third digit expresses ones, tens and hundreds digit .
The international system is followed by most of the countries of the world. In this system, a number is split up into groups or periods. In the Inter-national System of Numeration, we use ones, tens, hundreds, thousands, millions and billions.
The 1st period consists of —> ones, tens and hundred.
The 2nd period consists of —> thousand, 10 thousand and 100 thousands.
The 3rd period consists of —> million, 10 million and 100 million.
The 4th period consists of —> billion, 10 billion and 100 billion.
Example : The number 20,601,594 is read as twenty million, six hundred and one thousand, five hundred and ninety four.
Note:
Commas are used to mark thousands and millions. It comes after every three digits from the right. The first comma marks thousands and the next comma marks millions.
Properties of Natural Numbers
(i) Natural numbers are also called counting numbers.
(ii) The first and the smallest natural number is 1 (one).
(iii) Every natural number (except 1) can be obtained by adding 1 to the previous natural number.
(iv) For the natural number 1, there is no ‘previous’ natural number (Though 1 = 0 + 1, but 0 is not a natural number).
(v) There is no last or greatest natural number since they are infinite.
(vi) Natural numbers are denoted by 'ℕ' normally.=
(vii) We cannot complete the counting of all natural numbers. We express this fact by saying that there are infinitely many natural numbers.
Note:
The counting numbers 1, 2, 3, 4, ….. are called naturals numbers. The set of natural numbers is denoted by 'ℕ'. Thus, ℕ = {1, 2, 3, 4, …..}.
Even Natural Numbers (E):
A system of naturals numbers, which are divisible by 2 or are multiples of 2, is called a set of even numbers. It is denoted by 'E'.
Thus, E = {2, 4, 6, 8, 10, 12, …..}
There are infinite even numbers.
Odd Natural Numbers (O):
A system of naturals numbers, which are not divisible by 2 or are not multiples of 2, is called a set of odd numbers. It is denoted by 'O'.
Thus, O = {1, 3, 5, 7, 9, 11, …..}
There are infinite odd numbers.
Taking together the odd and even numbers, we get Natural Numbers.
Divisibility
"Divisible By" means "when you divide one number by another the result is a whole number
If we divide 14 by 7, we get 2. Thus, 2 and 7 are "Factors of 14 as by multiplying them, we get 14.
Take 40, for example. 1,2,4,5,8,10,20,40 are all factors of 40, as multiplying them with a certain number gives 40.
On the other hand, multiples are the result of multiplying any two digits.
For example, 14 is a multiple of 2 and 7. 40 is a multiple of 1,2,4,5,8,10,20,40.
A prime number (or a prime) is a natural number greater than 1 that has no positive divisors or factors other than 1 and itself.
For example, 5 is prime because 1, and 5 are its only positive integer factors.
A composite is a natural number greater than 1 which has a positive factor other than 1 and itself. For example, 6 has a factor of 1,2, 3 and 6 itself.