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28 is a perfect number. Add the factors of the number, excluding the number itself. 28: 1 +2 +4 + 7 + 14 = 28. The sum of its factors is the same as the number! The next perfect numbers are 496, 8128, 33550336, 8589869056, 137438691328, 2305843008139952128, 2658455991569831744654692615953842176, and 191561942608236107294793378084303638130997321548169216. Chances are that you won't be using that!
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Find perfect number less than forty?
6 and 28
Is 28 a perfect number?
Yes it is. 6 is the first perfect number, 28 is the second perfect number.
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.
How many integers less than 100 have an odd number of factors?
There are 9 integers less than 100 that have an odd number of factors.Every factor of a number has a pair, eg 2 & 3 are a factor pair of 6; and so it would be expected that every number has an even number of factors.However, if the factor pair of a number are the same number (eg 6 & 6 are a factor pair of 36), then there will be an odd number of factors.When there is a repeated factor like this, the number is a perfect square.Thus only perfect squares have an odd number of factors.Less than 100 there are 9 perfect squares (1, 4, 9, 16, 25, 36, 49, 64 & 81) which have an odd number of factors.100 itself is a perfect square and also has an odd number of factors, but the question asked for those numbers less than 100 with an odd number of factors.
Is 50 near a perfect number?
No, it is not near a perfect number. The first four known perfect numbers are 6, 28, 496 and 8,128.
