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 | 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! Shannon really is my favourite.
  • 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.
Click here to enter your comments.

If you don't have the time to provide feedback we'd really appreciate it if you could give this page a score! We are constantly improving and adding to these starters so it would be really helpful to know which ones are most useful. Simply click on a button below:

Excellent, I would like to see more like this
Good, achieved the results I required
Didn't really capture the interest of the students
Not for me! I wouldn't use this type of activity.

This starter has scored a mean of 3.2 out of 5 based on 451 votes.

Previous Day | This starter is for 3 March | Next Day



Your access to the majority of the Transum resources continues to be free but you can help support the continued growth of the website by doing your Amazon shopping using the links on this page. Below is an Amazon search box and some items chosen and recommended by Transum Mathematics to get you started.


Hello World

You are buying a (driverless) car. One vehicle is programmed to save as many lives as possible in a collision. Another promises to prioritize the lives of its passengers. Which do you choose?

Welcome to the age of the algorithm, the story of a not-too-distant future where machines rule supreme, making important decisions – in healthcare, transport, finance, security, what we watch, where we go even who we send to prison. So how much should we rely on them? What kind of future do we want?

Hannah Fry takes us on a tour of the good, the bad and the downright ugly of the algorithms that surround us. In Hello World she lifts the lid on their inner workings, demonstrates their power, exposes their limitations, and examines whether they really are an improvement on the humans they are replacing. more...

Online Maths Shop

Laptops In Lessons

Teacher, do your students have access to computers?
Do they have iPads or Laptops in Lessons?

Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Laptops In Lessons

Here a concise URL for a version of this page without the comments.

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.)


©1997-2019 WWW.TRANSUM.ORG