Skip to main content

Number System ( Basics )

NUMBER SYSTEM



TYPES OF NUMBERS

1. Natural Numbers: Numbers starting from 1, 2, 3, .......... are Natural Numbers.

2. Whole Numbers : Numbers starting from 0, 1, 2, 3, .......... are Whole Numbers. 

3. Integers : Negative, Zero and Positive Numbers comes in category of Intergers. 

     Ex. : -3, -2, -1, 0, 1, 2, 3, etc.

4. Negative Numbers : Numbers like -1, -2, -3, -4 ......... are Negative numbers

5. Positive Numbers : Numbers like 1, 2, 3, 4, .....are Positive Numbers.

6. Rational Numbers : Numbers that are being expressed in the form of p/q.

7. Irrational Numbers : An infinite Non-Recurring , Non - Terminating Decimal Number . Such numbers can't be expressed in the form of p/q.

8. Even Numbers : Numbers that are divisible by 2.

9. Odd Numbers : Numbers that can't be divisible by 2.

10. Prime Numbers : Numbers that are divisible by 1 or itself.   

 NOTE : 2 is only even prime number.
              There are 25 prime numbers upto 100. (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97)

11. Co- Prime Numbers : Pair of numbers are considered to be prime if their H. C. F. is 1. 

       Ex.:  5 and 12 are co - prime to each other.
             Consecutive Numbers are co-prime pairs.
             All prime numbers are co-prime pairs.

12. Composite Numbers : Numbers having factors other than itself and 1.

       NOTE : 1 is neither a composite number nor a prime number.

13. Real Numbers : Natural Numbers, Integers, Whole Numbers, Rational Numbers and Irrational Numbers constitutes set of Real Numbers. 

14. Perfect Numbers :  If sum of all the factors of a number excluding itself is equal to the number 

      Ex.:  6 is the first perfect number.  (1 + 2+3)
       Next three perfect Numbers are 28, 496, and 8128

Comments

Post a Comment

Popular posts from this blog

Number System (No. of Zeros)

  How to Find Number of Trailing     Zeros in a Factorial or Product Under the topic of Number of Zeros , it is expected to find out the number of trailing zeros at the end of the number. In simple words, it can be said that to calculate the No. of Zeros at the  right side of the number. To make the things more clear, let us take a simple example to understand the concept of Number of Zeros Example : 1234057000 → No. of Trailing zeros →  3                  1050500000 → No. of Trailing zeros → 5                  1.5 x 10⁵ → No. of Trailing zeros → 4 Such Zeros that are represented at the end of the numbers are actually the Trailing Zeros. Now the next thing arises about the formation of Zeros in the Numbers. So, the fundamental regarding the formation of a Zero is the presence of a Pair of ...
1 comment
Read more

Digital Sum Balance (D.S.)

A single digit is obtained by adding all the digits of a number is called Digital Sum Balance (D.S.)   Ex :  12 → 1 + 2 → 3 24 → 2 + 4 → 6 21 → 2 + 1  → 3 9876 → 9 + 8 + 7 + 6 → 30 → 3 + 0 → 3 3452 → 3 + 4 + 5 + 2 → 14 → 1 + 4 → 5 Or,  On Dividing the digits by 9, the obtained Remainder is Digital Sum Balance.  Ex :    12    ━━ = 3                9      24 ━━━ = 6      9    3452 ━━━━ =  5      9 KEY HIGHLIGHTS : The range of D.S. always falls from 0 to 9. When we add 9 to a number, its Digital Sum will not change therefore in order to calculate Digital Sum we need to cancel out  all the 9’s.  9 + 1 → 10 → 1 9 + 2 → 11 → 2 9 + 3 → 12 → 3 9 + 4 → 13 → 4 9 + 5 → 14 → 5 9 + 6 → 15 → 6 9 + 7 → 16 → 7 9 + 8 → 17 → 8 9 + 9 → 18 → 9 Example : 123 45 → 6 → Digital Sum ...
Post a Comment
Read more

HCF and LCM

HCF and LCM FACTORS / DIVISORS = Numbers that divide any number completely, without leaving any Remainder are its factors. Example : Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.                    Factors of 90 are 1, ,2, 3, 5 , 6, 9, 10, 15, 18, 30, 45, 90 MULTIPLES =   Numbers that fall in tables of any given number are its Multiples. Examples  : Multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96……                       Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 ….. HIGHEST COMMON FACTOR (H.C.F.) /  GREATEST COMMON DIVISOR (G.C.D.) =   Largest number that divides two or more than two given numbers. Examples : Calculate the  H.C.F. of 45 and 27  Sol : Factors of 45 = 1, 3, 5, 9, 15, 45       ...
Post a Comment
Read more