INAUSPICIOUS NUMBER 13?

        A popular maxim states that the best way to predict the future is to look into the past. History has repeatedly proven the number 13 to be a diabolical entity. sneaking in corners, ready to cause bad omens and accidents, so much so that the fear of this number over the centuries has compounded manifold to the point of causing looks of horrors at the prospect of residing at the "13th floor" of a building.

            The fear of this number has its own personalized jargon known as "Triskaidekaphobia". It is a combination of the Greek words "tris", meaning "three", "kai", meaning "and", "Deka" meaning "ten" and "phobia" meaning "fear".

* Apollo 13 was launched on 11 April and it underwent an explosion on the 13th of April (2 thirteens).

* Zoroastrian tradition predicts chaos in the 13th millennium.

*Another example is the Columbia Space Shuttle. This one went into space on 1/16/2003. Add all the numbers and you will get the number 13. During its re-entry into Earth, it exploded. All the crew members died.

* Many hotels in China and America don't have a 13th floor, After 12th, either they have 12 and a half or 14th. The same goes for the number of houses too.

* Even Microsoft considers the number 13 very unlucky and that is the reason why there is no

version 13 of Microsoft office. Version 12 is Microsoft Office 2007 and the next version Microsoft Office 2010 is actually version 14. Thus, the company skipped the number 13 altogether. 

But just because some superstition is blindly acknowledged, does it make it true? Does this number really deserve this notoriety?

** In ancient Greece, Zeus is considered as the thirteenth and the most powerful God. This thirteenth God seems to be associated with totality, completion, and attainment.

** The ladder to eternity has thirteen steps, on reaching the 13th step, it is assumed that your soul attains spiritual completion.

** 13 is a prime number, which means it cannot be divided by any number other than itself. Hence, Symbolizes qualities of incorruptible nature and purity.

** in one of the most powerful civilizations of history, the Aztecs decided to have 13 days in a week as they considered 13 to him an extremely lucky number. Each day was ruled by one God. And the God who ruled the thirteenth day was associated with mystery, psyche, and magic.

** As we all know 13 is the age of change or transition for every girl or boy. It is the age when children officially become teenagers.

** The US flag has 13 strips, that represent the union of 13 colonies to fight British rule, later these 13 colonies became the first thirteen states of the United States of America.

**The Thai New Year (Songkran Day) is celebrated on the 13th of April. It is considered to be a day of washing away all the bad omens, by splashing water on people, friends, and relatives.

** In Hindu mythology. MahaShivratri is celebrated on the thirteenth night of the Magha month. which is very sacred and a holy night for all the Shiva devotees.

** In the sacred book of the Sikhs, the "Guru Granth Sahib", the word "Waheguru" which means eternal guru appears 13 times.

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Ramanujan Number

1729 is called as the "Ramanujan Number".

This is also called as the TAXI CAB number.

The number which can be expressed as the sum of cubes of two different digits is called as the Taxi Cab Number.

example:- 2, 1729, 87539319 etc.

1729 is the smallest number that can be expressed as the sum of cubes of two numbers in two different ways.

There is an interesting story why these number called so.

Let's see.

Godfrey Hardy was a professor of Mathematics at Cambridge University.

One day he went to meet the great Indian Mathematician 

Srinivasa Ramanujan by a Taxi.

When Ramanujan heard that Hardy had come in a taxi he asked him what the number of the taxi was. Hardy said that it was just a boring number: 1729. Ramanujan replied that 1729 was not a boring number at all: it was a very interesting one. He explained that it was the smallest number that could be expressed by the sum of two cubes in two different ways.

This story is very famous among mathematicians. 1729 is sometimes called the “Hardy-Ramanujan number”.

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Divisibility Rules

Divisible by 2

If the unit digit of the number is even then the number is divisible by 2.

or

Any number whose unit digit is 0, 2, 4, 6 or 8 then the number is divisible by 2.

example: 892, 3648, 7936, 5566914, 22340 etc.

Divisible by 3

If the sum of all digits of a number is divisible by 3, then the number is divisible by 3.

example: 

i) 897121

sum of unit digits 8+9+7+1+2+1=28

since 28 is not divisible by 3, 897121 is not divisible by 3.

ii) 562137

sum of digits 5+6+2+1+3+7=24

since 24 is divisible by 3, 562137 is also divisible by 3.

Divisible by 4

If the last two digits of a number is divisible by 4, then the number is divisible by 4. 

Last two digits of the number can be 00, 04, 08, 12, 16, 20, 24...,96

example: 764, 82540, 369292, 879684, etc.

Divisible by 5

If the last digit of a number is either  5 or 0, then the number is divisible by 5.

example: 110, 265, 33845, etc.

Divisible by 6

If a number is divisible by both 2 and 3, then the number is divisible by 6.

Or

The even number which is divisible 3 is also divisible by 6.

example: 8640, 7656, 105936 etc.

Divisibility by 7

Multiply the digit of unit place by 2 and subtract from the remaining part of that number. If the resultant number is divisible by 7 then the number is divisible by 7.

example:- 

i) 405

The unit digit is 5 and remaining part of the number is 40.

40-5*2=30

since 30 is not divisible by 7, 405 is also not divisible by 7.

ii) 924

The unit digit is 4 and remaining part of the number is 92.

92-4*2=84

7 divides 84, so 924 is also divisible by 7.

Divisibility by 8

If the number formed by the last three digit of the given number is divisible by 8 then the actual number is divisible by 8.

The last three digit of the number can be 000,008,016,032,064,....,096,104,112,.....,992.

example:-

889344

number formed by last three digit of the given number is 344.

Since 344 is divisible by 8.

Hence 889344 is divisible by 8.

Divisibility by 9

If the sum of digits of the given number is divisible by 9, then the number is divisible by 9.

example:

i) 986321

sum of digits is 9+8+6+3+2+1=29

since 29 is not divisible by 9, hence 986321 is also not divisible by 9.

ii) 7648128

sum of digits 7+6+4+8+1+2+8=36

since 36 is divisible by 9, hence 7648128 is also divisible by 9.

Divisibility by 10

If the last digit of the number is zero, then the number is divisible by 10.

example: 70, 1520, 3548520 etc.

For any query comment below.

Thank you.

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