Divisibility

  • Oh! Hidden Inside?
    problem

    Oh! Hidden Inside?

    Age
    11 to 14
    Challenge level
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    Find the number which has 8 divisors, such that the product of the divisors is 331776.

  • Legs Eleven
    problem
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    Legs Eleven

    Age
    11 to 14
    Challenge level
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    Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

  • Place value, integers, ordering and rounding - Short Problems
    problem

    AB Search

    Age
    11 to 14
    Challenge level
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    The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?

  • Peaches today, Peaches tomorrow...
    problem
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    Peaches Today, Peaches Tomorrow...

    Age
    11 to 14
    Challenge level
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    A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?

  • Power mad!
    problem
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    Power Mad!

    Age
    11 to 14
    Challenge level
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    Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

  • What numbers can we make now?
    problem
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    What Numbers Can We Make Now?

    Age
    11 to 14
    Challenge level
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    Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

  • Four playing cards on top of each other. Each card shows a different ace.
    problem
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    Snappy Statements

    Age
    11 to 14
    Challenge level
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    You'll need to know your number properties to win a game of Statement Snap...

  • Differences
    problem
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    Differences

    Age
    11 to 14
    Challenge level
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    Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

  • Factoring factorials
    problem

    Factoring Factorials

    Age
    11 to 14
    Challenge level
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    Find the highest power of 11 that will divide into 1000! exactly.

  • Powerful factorial
    problem

    Powerful Factorial

    Age
    11 to 14
    Challenge level
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    6! = 6 × 5 × 4 × 3 × 2 × 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4) = 45. What is the highest power of two that divides exactly into 100!?