Thursday, October 6, 2011

Numbers and Means! (*)


Abundant numbers: Numbers where the sum of the factors, excluding the number itself, are greater than the number. (Also know as Excessive numbers. Every multiple of a Perfect number or Abundant number will also be an Abundant number.)
EX:  12 < (1+2+3+4+6)
Deficient numbers: Numbers where the sum of the factors, excluding the number itself, are less than the number.
EX: 10 > (1+2+5)
Perfect numbers: Numbers where the sum of the factors, excluding the number itself, equal the number.
EX: 6 = (1+2+3)
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Geometric mean: If you have n numbers, multiply the numbers together and take the nth root.
EX: Geometric mean of 6 and 7 = (6x7)^1/2
Harmonic mean: If you have n numbers, take the reciprocal of each number, add these fractions together, and divide n by this total.
EX: Harmonic mean of 6 and 7 = 2/(1/6 + 1/7)
Arithmetic mean: If you have n numbers, add the numbers together and divide by n.
EX: Arithmetic mean of 6 and 7 = (6+7)/2