Make your own free website on Tripod.com

Mathematics Friend's Club

Home
Questions
Some Facts
Thank you
Some Facts

1. The factors of 28 (not including itself) are 1, 2, 4, 7 and 14. Astonishingly these factors add up to give 28. Because 28 has this special property it is called a Perfect Number. 28 = 13 + 33 and so is also the sum of the first two odd cubes. Calculate 13 + 33 + 53 + 73. Find all the factors of this number. Is the number perfect?
_____________________________________________________
 
2. Since 32 + 42 = 52 does it follow that 33 + 43 + 53 = 63 ? Check it out !!
_____________________________________________________
 
3. Continue with these calculations and .... be amazed!
1x9 + 2 = 11
12x9 + 3 = 111
123x9 + 4 = 1111
_____________________________________________________
 
4.
3 x 37 = 111 and 1+1+1 = 3
6 x 37 = 222 and 2+2+2 = 6
9 x 37 = 333 and 3+3+3 = 9
...
continue this pattern and be amazed!
_____________________________________________________
 
5. How can you tell if a number divides by 11?
Answer: Alternately add and subtract the digits from right to left.
If the answer divides by 11 then so does the original number
Let's check 1999: 9-9+9-1=8 so it doesn't divide by 11.
Let's check 2013: 3-1+0-2=0 so it does divide by 11 ( since 0 divides exactly by 11).
Let's check: 723456789: 9-8+7-6+5-4+3-2+7=11 so it does divide by 11.
_____________________________________________________
 
 
6. In the decade 1990-1999 three of the years were prime:
1993 , 1997 and this year 1999.
Since all primes other than 2 and 5 end in either 1, 3, 7 or 9 then this decade has been RICH in primes.
The most prime years possible in a decade is four. The last such VERY RICH decade was 1800-1899:
1801, 1803, 1807 and 1809 are all prime.
An amazing fact is that there has been no VERY RICH decade for one hundred years.
In fact the current RICH decade is the first since 1780-1789:
1783, 1787 and 1789 are all prime.
So how long do you have to wait until the next RICH or VERY RICH decade? Will it be in your lifetime?
The good news is that if you are of school age just now you may just experience the next VERY RICH decade.
However the bad news is that you will definitely not experience another RICH decade like the present one.
So when are they? Search for yourself in the The Prime List.
 
 

Have more facts! Mail it to bappa123@gmail.com and we will post it in this site with your name.

Windows Web Hosting - ASP .NET Hosting