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**.