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.