Eleven (11)
1. Its
etymology originates from a German compound ainlif
meaning one left.
2. Eleven
is the only palindromic prime with an even number of digits.
3. It
can be portioned in 56 ways
4. It is a Lucas Number. The numbers in Lucas
series are 1, 3, 4, 7, 11…
5. It
is the fourth number that stays the same when written upside down. The first
three are 0, 1 and 8. The others such numbers less than 100 are 69, 88, 96.
6. The
sun spot cycle repeats every 11 years. Sun spots are dark areas on the surface
of the sun which have strong magnetic field.
7.Any
power of 11 ends with 1. 112 =121 113
=1331
8.The
magical sum of this magic triangle is 11.
9. It
is the smallest three digits prime in ternary system and four digit prime in
binary system. 11 in ternary system is written as (102)3 and in
binary as (1011)2.
10. It
is the fourth Sophie Germain Prime. A prime number p is a Sophie Germain prime
if 2p+ 1 is also a prime. The first ten Sophie Germain primes are 2, 3, 5, 11,
23, 29, 41, 53, 83 and 89.
11. It is a Stormer number. A Stormer number is a
positive integer n for which the greatest prime factor of n2 + 1
meets or exceeds 2n. It is named after Carl Stormer. The first eight Stormer
numbers are 1, 2, 4, 5, 6, 9, 10, and 11.
12. When
you divide a number with 11 in denominator it will have two digit repeating
sequences in their decimal expansion.
1/11
= 0.090909.. 2/11
= 0.181818..
3/11
= 0.272727... 4/11 =
0.363636..
13. Divisibility
by 11:- There are several methods to check the divisibility of a number by 11
but the most common amongst them is to alternately add and subtract digits
starting from the right. If the result thus obtained is the multiple of 11 then
the original number will be divisible by 11. Example:-Is 1331 divisible by 11? Here,
1 – 3 + 3 – 1 = 0, hence it is divisible by 11.
Rajesh Kumar Thakur
rkthakur1974@gmail.com
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