Tuesday, October 01, 2013

Deficient, Perfect, and Abundant

Deficient Numbers, Perfect Numbers,
and
Abundant Numbers


Did you know:  When you factor 945 into it's prime factors you get:

945 = 5 * 189
    = 5 * 3 * 63 
    = 5 * 3 * 7 * 9
    = 5 * 3 * 7 * 3 * 3

So { 3,3,3,5,7 } is the set of 'Prime Factors of 945

Also the 'Proper Factors' of 945 (i.e. ALL the numbers that divide evenly into 945 excepting 945 itself) make the set:

{ 1,3,5,7,9,15,21,27,35,45,63,105,135,189,315 }

And the sum of these proper factors is 975 (which is larger than 945).

Note-1: Numbers that are such that the sum of their proper factors is greater than the number are called "Abundant Numbers"

Note-2: Numbers that are such that the sum of their proper factors is equal to the number are called "Perfect Numbers"

Note-3: Numbers that are such that the sum of their proper factors is less than the number are called "Deficent Numbers"

And finally 945 is the smallest, odd, Abundant Number.