Factors and multiples

  • Common Divisor
    problem
    Favourite

    Common Divisor

    Age
    14 to 16
    Challenge level
    filled star empty star empty star
    Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.
  • Em'power'ed
    problem
    Favourite

    Em'power'ed

    Age
    16 to 18
    Challenge level
    filled star filled star empty star
    Find the smallest numbers a, b, and c such that: a^2 = 2b^3 = 3c^5 What can you say about other solutions to this problem?
  • Fac-Finding
    problem
    Favourite

    Fac-Finding

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful.
  • problem
    Favourite

    Biscuit Decorations

    Age
    5 to 7
    Challenge level
    filled star empty star empty star

    Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

  • Share Bears
    problem
    Favourite

    Share Bears

    Age
    5 to 7
    Challenge level
    filled star empty star empty star

    Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

  • Same Length Trains
    problem
    Favourite

    Same Length Trains

    Age
    5 to 7
    Challenge level
    filled star empty star empty star

    How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?

  • Clapping Times
    problem
    Favourite

    Clapping Times

    Age
    5 to 7
    Challenge level
    filled star empty star empty star

    If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?

  • Lots of Biscuits!
    problem
    Favourite

    Lots of Biscuits!

    Age
    5 to 7
    Challenge level
    filled star empty star empty star

    Help share out the biscuits the children have made.

  • I Like ...
    problem
    Favourite

    I Like ...

    Age
    5 to 7
    Challenge level
    filled star empty star empty star

    Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

  • Our Numbers
    problem
    Favourite

    Our Numbers

    Age
    5 to 7
    Challenge level
    filled star empty star empty star

    These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?