# Number Series For HPTET Non Medical Exam

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Number : It is an idea which tells us how many  objects are there in a collection.

Numeral : It is a symbol by means of which a number is represented.

Unit : A unit represented a single thing, as nine  pencils, twelve articles, twenty kilograms.

Natural Number and Whole Number: Natural  numbers (i.e. 1. 2. 3. 4.....) are the numbers used for counting, where as whole numbers (ie. 0, 1, 2, 3,  4,....) are the numbers used for counting and also including zero.

Integers: These are the numbers represented with positive or negative sign (i.e. -1, -3, -5,0,7,9)

Prime Number and Composite Number : Prime number is a natural number, other than 1, which has no other factor than 1 and itself e.g. 2, 3,  5, 7, 11, 13..... are prime numbers. Composite number is a natural number different from 1, which has atleast  one factor other than 1 and itself, e.g, 4, 6, 8, 9,...  are composite numbers.

Even Numbers and Odd Number: Even numbers are the numbers completely divided by 2,

e.g. 2, 4, 6, 8.... Whereas odd numbers are the numbers incompletely divided by 2, e.g. 1, 3, 5, 9.

Rational and Irrational Numbers: Rational numbers can be expressed in the form x/y,where a and y are integers and y is not equal to 0.3/4,0.3/11.9/4 etc.  are rational numbers. On the other hand, irrational  numbers cannot be expressed in the form of x/y,e.g under root 3,3 under root 7

Real Numbers : The real number system consists of all the rational numbers and irrational numbers.

1. A real number whose decimal representation is either terminating decimal or non-terminating but repeated decimal is called a rational number.

2. A real number whose decimal representation is non-terminating and non-repeating is called an irrational number.

Dividend, Divisor and Quotient: If a number is divided by another number, then

1. Dividend = Divisor Quotient + Remainder, where O < =Remainder <Divisor

2. Divisor = Dividend - Remainder/Quotient

3. Quotient =Dividend - Remainder/Divisor

4. Dividend - Remainder = Quotient Divisor

Divisibility Test

1. A number is divisible by 2, if its last digit is zero or an even number Examples : 714, 9632, 930 etc.

2. A number is divisible by 3, if the sum of its digits is divisible by 3. Examples: 132, 747, 5436 etc.

3. A number is divisible by 4, if its last two digits are 00 or divisible by 4. Examples: 1400, 4372, 7712 etc,

4. A number is divisible by 5, if its last digit is zero or five. Examples: 150, 175, 3945 etc.

5. A number is divisible by 6, if it is also divisible by 2 or 3 (or follow the conditions of divisibility

of 2 and 3). Examples: 330, 34200, 57312 etc.

6. A number is divisible by 7. if it consists of six times repeatition of a same digit. Examples : 222222, 333333, 999999 etc.

7. A number is divisible by 8, if its last three digits  are divisible by 8. Examples: 2008, 7824, 17648 etc.

8. A number is divisible by 9, if the sum of its digits is divisible by 9. Examples : 738.9432, 10071 etc.

9. A number is divisible by 10, if its last digit is 0. Examples : 510, 1710, 56940 etc.

10. A number is divisible by 11, if the difference between the sum of the digits in the odd places and the sum of the digits in the even places is either divisible by 11 or equal to zero. Examples : 5943322, 948393721, 103994 etc.

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