Question

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What is perfect number? Give at least 5 examples.

Answer 1

Hey

Definitions:-

A perfect number, N, is equal to the sum of all its proper divisors. ( including 1) or we can say A Perfect Number N is defined as any positive integer where the sum of its divisors minus the number itself equals the number. The first few of these, already known to the ancient Greeks, are 6, 28, 496, and 8128.


The first perfect number is 6. Its proper divisors are 1, 2, and 3, and 1 + 2 + 3 = 6. Equivalently, the number 6 is equal to half the sum of all its positive divisors: ( 1 + 2 + 3 + 6 ) / 2 = 6. The next perfect number is 28 = 1 + 2 + 4 + 7 + 14.

For example, the first four perfect numbers are generated by the formula 2p−1(2p − 1), with p a prime number, as follows:

for p = 2:   21(22 − 1) = 6for p = 3:   22(23 − 1) = 28for p = 5:   24(25 − 1) = 496for p = 7:   26(27 − 1) = 8128.

Its proper divisors are 1, 2, and 3, and 1 + 2 + 3 = 6. Equivalently, the number 6 is equal to half the sum of all its positive divisors: ( 1 + 2 + 3 + 6 ) / 2 = 6. The next perfect number is 28 = 1 + 2 + 4 + 7 + 14. This is followed by the perfect numbers 496 and 8128 

Answer 2

hy

here is your answer bro
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A perfect number is a positive number that equals the sum of its divisors, excluding itself. This is also known as its aliquot sum. At this time, it is unknown how many perfect numbers truly exist in our number system. While we have discovered 48 perfect numbers

A Perfect Number N is defined as any positive integer where the sum of its divisors minus the number itself equals the number. The first few of these, already known to the ancient Greeks, are 6, 28, 496, and 8128.

example :- The first perfect number is 6. Its proper divisors are 1, 2, and 3, and 1 + 2 + 3 = 6. Equivalently, the number 6 is equal to half the sum of all its positive divisors: ( 1 + 2 + 3 + 6 ) / 2 = 6.

example2:-The next perfect number is 28

28 = 1 + 2 + 4 + 7 + 14.

example3: Find out if  496 is  a perfect number

The proper factors of 496 are 1, 2, 4, 8, 16, 31, 62, 124, and 248

1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 496

496 is perfect.

another example in pic