Perfect number is a special type of number, where the sum of all the factors of it, except the number itself, yields the number itself. For example:- 6 is a perfect number. Because sum of all the factors of 6 except 6 yields 6( 1 + 2 + 3 = 6).
All the perfect numbers end with the digit 6 or 8.
All the perfect numbers are even numbers. But all the even numbers are not perfect numbers.
It is still not known to humankind, whether there are any odd perfect numbers.
All the perfect numbers are in the form of 2p−1× (2p − 1)) . Where P is a non-zero number.
As per 2018, around 50 perfect numbers were known to us. Some of the known perfect numbers are as follows.
6 (1 + 2 + 3 = 6)
28 (1 + 2 + 4 + 7 + 14 = 28)
496 (1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 496)
8128 (1 + 2 + 4 + 8 + 16 + 32 + 64 + 127 + 254 + 508 + 1016 + 2032 + 4064 = 8128)
Some bigger perfect numbers are as follows:-
33 550 336 (8 digits)
8 589 869 056 (10 digits)
137 438 691 328 (12 digits)
2 305 843 008 139 952 128 (19 digits)
2 658 455 991 569 831 744 654 692 615 953 842 176 (37 digits)
191 561 942 608 236 107 294 793 378 084 303 638 130 997 321 548 169 216 (54 digits)
13 164 036 458 569 648 337 239 753 460 458 722 910 223 472 318 386 943 117 783 728 128 (65 digits)
14 474 011 154 664 524 427 946 373 126 085 988 481 573 677 491 474 835 889 066 354 349 131 199 152 128 (77 digits)
HAPPY LEARNING……………………………