Perfect Numbers

A Maths Lesson Starter Of The Day

Perfect six

The factors of six are 1, 2 and 3 (not including six itself)

Add up these factors and you will get six:

1+2+3 = 6

Six is a perfect number as it is the sum of its factors. Can you find any other perfect numbers?

Topics: Starter | Factors | Number

  • Mrs. Alabame, DS Masone School, Pretend
  • Well, being a year 6 class we only had time to do short starter as we had to do some revision for the up and coming SAT's. I ended up giving points to the young girl who first got 28! Well done Shannon.
  • Class 1.4, Brechin High School
  • Finding perfect numbers is a perfect start to World Maths Day, don't you agree?
  • Apex Secondary School, Year 12
  • My class got all the perfect numbers and the last perfect number zaid got he is even better then me!
  • Mr Jennings, Balshaws CE High School
  • What a great starter. Joseph smashed it in 1. What a star!!!
  • Transum,
  • Do the perfect numbers have any other purpose or meaning? Apparently ancient civilisations gave religious and magical significance to the perfect numbers. One example is that God chose to create the world in a perfect number of days (six). Others saw that the moon's period of 28 days was another perfect number connection. Stretching this line of thought to the third perfect number, the number 496 is a very important number in superstring theory. One of the necessary conditions for a superstring theory to make sense is that the dimension of the gauge group must be 496. But I’m sure you knew that already didn’t you?
  • Mrs Peters, Black Lane
  • Snowdon have been trying to find perfect numbers for the past 15 minutes and we can't find any perfect numbers. Is this a trick question?

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
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Laptops In Lessons

Teacher, do your students have access to computers such as tablets, iPads or Laptops?  This page was really designed for projection on a whiteboard but if you really want the students to have access to it here is a concise URL for a version of this page without the comments:

However it would be better to assign one of the student interactive activities below.

Laptops In Lessons

Here is the URL which will take them to a related student activity.

Student Activity

Related to perfect numbers are amicable numbers. Two numbers are amicable if the sum of the proper divisors of the first is equal to the second and vice versa. Sociable numbers form a closed sequence where the sum of the proper divisors of one number is equal to the next number in the sequence. The sum of the proper divisors of the last term of the sequence is equal to the first number. (A proper divisor of a number is a positive factor of that number other than the number itself. For example, the proper divisors of 10 are 1, 2, and 5.)

Curriculum Reference

See the National Curriculum page for links to related online activities and resources.


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