Saturday, July 4, 2015

Properties of Number 8


        Importance of  Eight (8)
1.      It is a composite number with its proper divisor being 1, 2 and 4.
2.      It is the base of the octal number system. In octal number system one digit represents 3 bits.
3.      The atomic number of oxygen is eight.
4.      Scorpio is the 8th astrological sign of the Zodiac.
5.      A map consists of 8 directions:- North, Northeast, Northwest, East, Southeast, Southwest, West, South.
6.      In three dimensional spaces there are 8 octants and the eight octants have the different co-ordinates shown here.
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7.      Apart from the trivial cases of 0 and 1, 8 is the smallest number for which the sum of the digits of its cube is equal to the number.                                                                                    
                    83         = 512  and 5 + 1 + 2 = 8
8.      It is the largest cube in the Fibonacci sequence. A Fibonacci number is a numbers in which the next number is the sum of previous two. 1, 1, 2, 3, 5, 8… are the numbers of the Fibonacci sequence.
9.      It is the second cube number. 23 = 8
10.  One can split a pie into 8 pieces with three straight cuts.

11.  A cube or cuboids has 8 vertices.

12.  An umbrella is octagonal in shape.    

13.  The digital sum of a prime pair product is 8.                                                                 
                          5 x 7 = 35 and 3 + 5 = 8                                                              
                          11 x 13 = 143 and 1 + 4 + 3 = 8                                                                               
                          17 x 19 = 323 and 3 + 2 + 3 = 8                                                                                 
                       29 x 31 = 899 and 8 + 9 + 9 = 26 and 2+ 6 = 8
14.  A number is divisible by 8 if it ends with 000 or its last three digit is divisible by 8. 
                          Example – 1000, 456640
15.  Many spiders, bees and flies have eight legs.

16.  Eight is the third number that remains the same written upside down.
17.  The amount of cloud in the sky is measured in oktas on a scale from zero to eight. 8 oktas means the sky is totally clouded.
18.  It is the second honest number.                                                                                                      
                23 = Two Cubed = 8 has eight letters.
19.  It is the smallest sum of two factorials of distinct primes.                                                              
                       2! + 3! = 2 + 6 = 8
20.  It is the only cube that is 1 less than a square.                                                                                  
                           8 = 32 – 1 
21.  Digit sum of prime pair product comes out 8.                                                                                  
                5 x 7 = 35                           and        3 + 5 = 8                                                                      
              11 x 13 = 143  and                                   1 + 4 + 3 = 8                                                                
              17 x 19 = 323  and      3 + 2 + 3 = 8
22.  Eight can be portioned in 22 ways.
23.  8 times any triangular number is 1 less than a square. 1, 3, 6, 10,… are the examples of triangular number. If we take 3 as a triangular number than 8x 3 = 24 is 1 less than 25 which is a square number.

24.  It is the second octagonal number represented by the formula n(3n – 2 ), where n is any natural number. The sequence is 1, 8, 21, 40….

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