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Do all numbers have an even number of factors?
No. Perfect square numbers have an odd number of factors.
What type of number has a n odd number of factors?
all perfect square numbers
What are perfact numbers?
If the sum of all a number's factors (factors that are smaller than the number itself) is equal to the number itself, the number is said to be "perfect". For example, the factors of 6 (excluding 6 itself) are 1, 2, and 3; and the sum of these numbers is exactly 6. The smallest perfect numbers are 6, 28, 496, 8128. It isn't known whether the set of perfect numbers is finite or infinite. Also, it isn't known whether there are any odd perfect number; all known perfect numbers are even.
What numbers always have an even number of factors?
All positive integers which are not perfect squares.
Are all multiples of abundant numbers abundant?
Yes, this is well known. All integral multiples of any perfect, or abundant number must be an abundant number.
