Factorials

  • Growing
    problem

    Growing

    Age
    16 to 18
    Challenge level
    Which is larger: (a) 1.000001^{1000000} or 2? (b) 100^{300} or 300! (i.e.factorial 300)
  • SquareSearch
    problem

    Squaresearch

    Age
    14 to 16
    Challenge level
    Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?
  • Forgotten Number
    problem

    Forgotten Number

    Age
    11 to 14
    Challenge level

    I have forgotten the number of the combination of the lock on my briefcase. I did have a method for remembering it...

  • Factoring factorials
    problem

    Factoring Factorials

    Age
    11 to 14
    Challenge level

    Find the highest power of 11 that will divide into 1000! exactly.

  • Powerful factorial
    problem

    Powerful Factorial

    Age
    11 to 14
    Challenge level

    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!?

  • Small tomato seedlings in pink pots.
    problem

    Trailing Zeros

    Age
    11 to 14
    Challenge level

    How many zeros does 50! have at the end?

  • N000ughty thoughts
    problem

    N000ughty

    Age
    14 to 16
    Challenge level

    How many noughts are at the end of these giant numbers?

  • Factorial
    problem

    Factorial

    Age
    14 to 16
    Challenge level

    How many zeros are there at the end of the number which is the product of first hundred positive integers?

  • Small tomato seedlings in pink pots.
    problem

    Factorised Factorial

    Age
    14 to 16
    Challenge level

    Weekly Problem 17 - 2010
    The value of the factorial $n!$ is written in a different way. Can you work what $n$ must be?

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