What is the longest sequence you can make from the numbers below?


Each number in the sequence must be a factor or multiple of the previous number.



Topics: Starter | Arithmetic | Factors | Mental Methods | Number

  • Transum,
  • This is a fascinating activity on a number of levels. It is accessible to pupils who have learned about factors and multiples and need practice but it also proves to be an interesting activity for older pupils who may analyse the situation from a more general perspective. Finding the best solution and being sure that it can't be bettered is a challenge for the most able. What strategies did your class come up with?
  • Mrs M,
  • Good to revise factors and multiples.
  • WKGS, Wirral
  • We got 18!
  • Paula, Portsmoiuth
  • I got 20!
  • Katy, Sydney
  • Got 21! Definitely going to this to extend my students.
  • Room 5, Cool School
  • WE got 21 too!! Took us afew goes but we think 21 is brilliant.
  • Mr S, Haslemere
  • We got 20, please post solution for 21.
  • Kai and Finn, 5M
  • Finn and I got 20. WOW!
  • Luca, Canberra, Australia
  • I got 20 but still working on it.
  • Oliver, Tenterden Joinior
  • Amazing I got the best score in my class 15.
  • Miss Collins,
  • This a really great starter for my class. It makes you think a lot.
  • Miss McElderry WMS, Twitter
  • ImagineMath,
  • Here's a solution for 21:
    {23, 1, 11, 22, 2, 14, 7, 21, 3, 9, 18, 6, 12, 24, 8, 16, 4, 20, 10, 5, 15}.
  • 9M4, Pudsey
  • 9M4 found 21 steps...had to start with a prime number nice challenge.
  • Year 6, Australia
  • This game is so fun, definitely recommended if you are learning factors and multiples. I can make a long chain but sometimes it is hard. Can you all the numbers?
  • Red Ho5 @NetZeroLee, Coppell, Texas
  • We loved this activity! Got 21!
  • MayV, Twitter

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 the game version of this activity.


Student Activity


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Student Activity



What is the longest sequence that can be generated if the numbers 1 to 100 are available?

See Flabbergasted Game.


Curriculum Reference

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


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