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Today is Day 24 of 2017

24

is smallest number with exactly eight divisors (1, 2, 3, 4, 6, 8, 12, 24), and the largest number with the following property: subtracting one from each of its divisors produces a prime number.

SOTP OOOPS!is the number of different ways in which the letters of 'STOP' may be arranged. Only 6 arrangements produce words, though.

Sotp? Oops... ->

= 210 - 103
= 72 - 52 (difference of squares)
= 4!
= 3 + 5 + 7 + 9 (sum of consecutive odd numbers)
= 25 - 23
= 33 - 31

24 = (2 + root4)!

Select any prime number equal or greater than 5, square it, subtract 1 from that, then the result is always divisible by 24. For instance, 372 - 1 = 1368 is divisible by 24. However, this works just as well with any odd number not divisible by 3. For instance, 1252 - 1 = 15624 is divisible by 24. In fact, any number of the form p2 - q2 can be divisible by 24, for p and q primes > 3.

The product of 4 consecutive numbers n(n+1)(n+2)(n+3) is divisible by 24.

There are 24 hours in a day.

Many thanks are extended to Archimedes' Lab for their information.




24

Today is day number   of 2017. Below are various representations of the number 24, some dating thousands of years, and some very modern.

Chinese

Egyptian

Mayan

 

Babylonian

Greek

Abacus

Roman

 

Hex

 

Binary

 

Many thanks are extended to Jo Edkins for her wonderful work.

 

 



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[Added June 2009]

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