Factors · Grades 5–8 · Unsolved

Odd Perfect Numbers

A number is perfect when its factors add up to it, like 6 = 1 + 2 + 3. Is any perfect number odd?

Bars show each number’s factors added up. The dark line is the number itself. Only 6 and 28 match exactly.

Try it

6 = 1 + 2 + 328 = 1 + 2 + 4 + 7 + 14Next: 496, then 8,128

About fifty perfect numbers are known. Every one is even.

People have wondered about odd ones for more than 2,000 years.

Sort 1 to 30: factors add to less, more, or exactly?

Can an odd number’s factors ever add to more than it? (Try 945.)

Detailed one-pager (PDF) History, why it’s unsolved, and more classroom ideas