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What is an abundant number?
There are three equivalent definitions for an abundant number.A number is abundant if:the sum of all its factors (including itself) is more than double the number;the sum of all factors of the number which are smaller than the number, must be more than the number;the sum of all proper factors of the number must be at least as large as the number.
What numbers are proper factors?
That means that one number is a factor of the other number, but that it's not the number itself. For example: the factors of 9 are 1, 3, and 9. The proper factors of 9 are 1 and 3.
How do you express a number as a product of its primes?
The first thing to do is to determine the proper prime factors. Proper means that you don't count the number itself, because every number is divisible by itself. You also don't count 1 for the same reason, and anyway 1 isn't really a prime.The proper factors you must note all of them. The proper prime factors of 24 are 2 2 2 3. There are only 2 different factors, but 2 goes in once and again and again. To express 24 as aproduct of its primes, it's just 2 x 2 x 2 x 3. You can also express it as 23 x 3.
What is true about balanced equations?
The amount on one side of the '=' must balance the amount on the other.
How are odd and even numbers are related to their factors?
Even numbers must have 2 amongst their factors; they may have other even numbers amongst their factors. Odd numbers must not; every factor of an odd number must be odd.
