Abundant and deficient numbers.

[Celsion]

What's a quick way to find abundant and deficient numbers?

Thanks for your help in advanced.

[Quelloquialism]

Memorize the first few perfects and abundants.

Perfects: 6, 28, 496, 8128, ...
Abundants: 20, 70, 88, ...

All multiples of perfects and abundants are abundant. Check the answer choices for divisibility.

[stupidityismygam]

well all multiples of perfect numbers are abundant numbers

otherwise, i would suggest just finding the sum of the factors

the trick is:

if you have a number [unparseable or potentially dangerous latex formula] where the RHS is the prime factorization of x, then

the sum of the factors of x is:

[unparseable or potentially dangerous latex formula]

so if that is > 2x then it is abundant, = 2x is perfect, < 2x is deficient

edit: change to b+1

[Celsion]

[Kurt]

[bradp]

as others said, check for divisibility by a perfect number
otherwise
look for a big prime factor in the factorization...

71 * 2 * 3 will have a lot less divisors (and therefore a smaller sum of divisors) than 2^3 * 3^3 * 5