Back To The Factory

An Advanced Mathematics Lesson Starter Of The Day

The following challenge appeared in Mathematical Pie, a Mathematical Association publication.

 

The prime factorisation of 600 is 23 x 52 x 3. We can make all the factors of 600 by choosing from four possibilities for the 2 (to include it 0, 1, 2 or 3 times); three possibilities for the 5 (to include it 0, I or 2 times) and two possibilities for the 3 (to include it or not).

Altogether 4 x 3 x 2 = 24 possibilities (if we don't choose any of the three this will give the factor l). So 600 has 24 factors.

 

Can you use the same idea to find all the numbers below 1000 which have exactly 20 factors?

Number Factory

Extension

The following challenge appeared in the book Math Girls by Hiroshi Yuki.

"Describe a method for summing the divisors
of a given positive integer n"

More Advanced Lesson Starters


Topics: Starter

    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.

    Previous Day | This starter is for | Next Day

     

    Answer

    More Advanced Lesson Starters

    More Mathematics Lesson Starters

    How did you use this resource? Can you suggest how teachers could present, adapt or develop it? 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.



    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 link. As an Amazon Associate I earn a small amount from qualifying purchases which helps pay for the upkeep of this website.

    Educational Technology on Amazon

     


    Transum.org is a proud supporter of the kidSAFE Seal Program