Home > Science Fact Finder > Mathematics, Numbers, and Computers - What Is A Perfect Number?

1. Printable Version
2. Download PDF
3. Cite this Page

What is a perfect number?

A perfect number is a number equal to the sum of all of its proper divisors. Proper divisors are all the divisors of a number with the exception of the number itself. The number 6 is the smallest perfect number; the sum of its divisors—1,2, and 3—equals 6. The next 3 perfect numbers are 28, 496, and 8,126. No odd perfect numbers are known. The highest established perfect number is: (2^859,433 -1) X 2^859,433.

Sources: Chambers Science and Technology Dictionary, p. 659; The Guinness Book of Records 1996, p. 73; McGraw-Hill Encyclopedia of Science and Technology, vol. 12, p. 241.

Join eNotes

The above is a free excerpt. Get total access to this content with the:

eNotes Pass

1. Mathematics
   1. What is the most enduring mathematical work of all time?
   2. Who discovered the formula for the area of a triangle?
   3. What are the common mathematical formulas for area?
   4. What are the common mathematical formulas for volume?
   5. When did the concept of square roof originate?
   6. What is the probability of a successful triple play occurring in a single baseball game?
   7. What is the Pythagorean theorem?
   8. How is Pascal's triangle used?
   9. What is the difference between a median, a mean, and a mode?
   10. How many feet are on each side of an acre that is square?
   11. What are the Platonic solids?
   12. What are "Napier's bones"?
   13. Who invented the slide rule?
   14. How long has the abacus been used? Is it still used?
   15. How is "casting out nines" used to check the results of addition or multiplication?
   16. What is Zeno's paradox?
2. Numbers
   1. What is the value of pi out to 30 digits past the decimal point?
   2. What is the largest prime number presently known?
   3. What are Roman numerals?
   4. Is it possible to count to infinity?
   5. What is a perfect number?
   6. How large is a googol?
   7. Why is seven considered by some to be a magical number?
   8. What are Fibonacci numbers?
3. Computers
   1. Who invented the computer?
   2. Who was the first programmer?
   3. What is a computer program?
   4. What does DOS stand for?
   5. What is meant by "fifth generation computers"? What are the other four generations?
   6. What is a fuzzy search?
   7. What is a silicon chip?
   8. Are any devices being developed to replace silicon chips?
   9. How is a byte defined?
   10. How is a hard disk different from a floppy disk?
   11. Why does a computer floppy disk have to be "formatted"?
   12. What is the lifespan of a CD-ROM disc?
   13. What is a pixel?
   14. Who invented the computer mouse?
   15. What is a computer "virus" and how is it spread?
   16. Where did the term "bug" originate?
   17. What is e-mail?
   18. What is a hacker?
   19. How do you position yourself correctly in front of a computer screen?
   20. What was the first successful video-arcade game?
   21. Should a personal computer be turned off when not in use?