composite number
64
A + 2a = 3a
1. List all factors of number (including 1 and the number, list each factor only once even if it goes in multiple times) 2. Add up all the factors 3. If the sum is equal to twice the original number, then the original number is perfect, if not, it is not perfect.
n + 2n = 3n
Because it's a square number. All perfect squares have an odd number of factors because they have one factor pair that is the same number twice (the square root) and when the factors are listed, the number is listed once.
There aren't any numbers like that. You might be thinking of 28, which has a sum of all its factors equal to twice itself, making it a perfect number. Proper factors are a different set.
multiply
Because the square root isn't listed twice.
The difference between a number x and twice y is equal to fifteen.
In a perfect number, the sum of all the factors (including the number itself) is twice the number. E.g., the sum of the factors of 6 is 1 + 2 + 3 + 6 = 12 (equal to 2 x 6). Every prime number has two factors: 1, and itself. So, the sum of the factors is only one more than the prime number itself; for any number greater than 1, this can't be twice the number. For example, the prime number 7 has the factors 1 and 7, which add up to 8.
64
A + 2a = 3a
Simple! The number is 0.
To find the primes that equal a number, start with any factor pair of the number and keep factoring the composite factors until all factors are prime. 44 2 x 22 2 x 2 x 11 = 44 The two prime numbers that equal 44 are 2 (twice) and 11.
It is not. A perfect number is defined as a number that is equal to twice the sum of all of its factors (or equal to all of its factors, smaller than the number itself). Perfect numbers include 6 (factors 1, 2, 3, 6) and 28 (factors 1, 2, 4, 7, 14, 28). It is not known whether there are odd perfect numbers. - Unless somebody is using a different definition of "perfect" in this case; but when you talk about a "perfect number", the above definition is commonly used.
um, 9.
Factors can be listed as factor pairs. With square numbers, one of those pairs will be the same number twice. When written as a list, only one of them will be used, leaving an odd number of factors.