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Fibonacci Quest

A number of self marking quizzes based on the fascinating Fibonacci Sequence.

Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Description Help More Sequences

This is level 5; Investigate the highest common factor of every nth term of the Fibonacci sequence..

What is the HFC of every3rd term4th term5th termetc.
, , , , , , , , , ,
  Correct Wrong Correct Wrong Correct Wrong Correct Wrong Correct Wrong Correct Wrong Correct Wrong Correct Wrong Correct Wrong Correct Wrong

With the exceptions of 1, 8 and 144, every Fibonacci number has a prime factor that is not a factor of any smaller Fibonacci number. This is known as Carmichael's theorem.

Fibonacci Rectangle
miles to kilometers

Here's a quick trick for roughly converting between miles and kilometres using the Fibonacci sequence.

To convert from miles to kilometers find the term of the sequence closest to the distance in miles. The next term in the sequence is an approximation of that distance in kilometres.

To convert from kilometres to miles find the term of the sequence closest to the distance in kilometres. The previous term in the sequence is an approximation of that distance in miles.

Can you explain why this trick works?

There is an online exercise providing practice converting between miles and kilometres here.

This is Fibonacci Quest level 5. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 6


Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

Please contact me if you have any suggestions or questions.

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Comment recorded on the 19 November 'Starter of the Day' page by Lesley Sewell, Ysgol Aberconwy, Wales:

"A Maths colleague introduced me to your web site and I love to use it. The questions are so varied I can use them with all of my classes, I even let year 13 have a go at some of them. I like being able to access the whole month so I can use favourites with classes I see at different times of the week. Thanks."

Comment recorded on the 28 May 'Starter of the Day' page by L Smith, Colwyn Bay:

"An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!"

Featured Activity

One Torch Tunnel

One Torch Tunnel

Solve the problem of getting four people through a tunnel with one torch in the minimum amount of time. The solution is not obvious but when you get it you see the elegance and beauty of its cunning.


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Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.


If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

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Description of Levels



Level 1 - Continue the basic Fibonacci sequence

Level 2 - Continue the Fibonacci sequence in reverse

Level 3 - Find algebraic expressions for each term of a Fibonacci sequence

Level 4 - Finding the ratio of two successive numbers in Fibonacci's sequence

Level 5 - Investigate the highest common factor of every nth term of the Fibonacci sequence.

Level 6 - Finding missing terms from Fibonacci-type sequences.

The Magic of Fibonacci Numbers

Arthur Benjamin gives a TED talk on Fibonacci numbers.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly.