When it comes to perfect numbers, there is a range of numbers from 1 to 100 that are known as perfect numbers. A perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. For example, the number 6 is a perfect number because it is the sum of 1, 2 and 3, which are its positive divisors (1 + 2 + 3 = 6).
The perfect numbers from 1 to 100 are 6, 28, 496, 8128, and 33,550,336. The number 6 is the smallest perfect number in this range, and it is the product of 1, 2 and 3. It is also the sum of all of its positive divisors, excluding itself (1 + 2 + 3 = 6).
The number 28 is the next perfect number in this range, and it is the product of 1, 2, 4, 7 and 14. It is also the sum of all of its positive divisors, excluding itself (1 + 2 + 4 + 7 + 14 = 28).
The number 496 is the third perfect number in this range, and it is the product of 1, 2, 4, 8, 16, 31, 62, and 124. It is also the sum of all of its positive divisors, excluding itself (1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 = 496).
The number 8128 is the fourth perfect number in this range, and it is the product of 1, 2, 4, 8, 16, 32, 64, 127, 254, and 508. It is also the sum of all of its positive divisors, excluding itself (1 + 2 + 4 + 8 + 16 + 32 + 64 + 127 + 254 + 508 = 8128).
The number 33,550,336 is the fifth perfect number in this range, and it is the product of 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, and 131072. It is also the sum of all of its positive divisors, excluding itself (1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 + 2048 + 4096 + 8192 + 16384 + 32768 + 65536 + 131072 = 33,550,336).
These five perfect numbers from 1 to 100 are the only perfect numbers in this range. All other numbers between 1 and 100 are either not perfect, or not known to be perfect. Every perfect number is the sum of its positive divisors, excluding itself, and the first five perfect numbers in this range are 6, 28, 496, 8128, and 33,550,336.
