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Perfect Numbers

There are different types of Numbers in the number system. Perfect Numbers are one of such types.  The perfect number is a positive number whose factors when added give back the number as answer. The factors of the numbers are less than the number.

Some examples of perfect numbers are given below:

1. The factors of number 6 are 1, 2 and 3.
1 + 2+ 3 = 6
So, 6 is a perfect number.

2. The factors of 28 are 1, 2, 4, 7, and 14.
1 + 2 + 4 + 7 + 14 = 28
So, 28 is a perfect number.

There are others such as 496, 8128 and many higher numbers.

In a perfect number, the product of its even factor and prime factor gives the number itself. The perfect numbers are both even and odd. But there is a confusion that whether a odd perfect number really do exist. Mathematician found one but it gives an approximate answer.

The formula for finding even perfect number is given as,
2(p-1) * (2p-1) where ‘p’ is the Prime Numbers and 2 p -1 is also a prime number.

Example:
Let us consider, p = 2 which is a prime number.
Then (23-1) = 7 which is also a prime number.
2(3-1) * (23- 1) = 28 is a perfect number.

The perfect numbers were used in ancient cultures and religion of certain regions. The perfect number are also used in computer science or computer application as a coding problem and it finds ways in generating these numbers using computer coding in different computer languages.

Perfect Number Definition

Perfect numbers definition states that perfect number is a positive Integer which is equals to addition of its proper divisors. We can also say that perfect number is equals to addition of half of all divisors. In a perfect number, the product of its even factor and prime factor gives the number itself.

First perfect number is 6 as its divisors are 1, 2...Read More

Odd Perfect Numbers

The number which is exactly divisible by two is known as even number and the number which is not divisible by two is known as odd number. A positive number which is equals to the sum of the positive divisors is known as perfect number.

Some examples of Perfect Numbers are given below:

1. The factors of number 6 are 1, 2 and 3.
1 + 2+ 3 = 6
So, 6 is a ...Read More

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