Prime numbers

  • Factor Trio
    problem

    Factor Trio

    Age
    11 to 14
    Challenge level
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    Which of the numbers shown is the product of exactly 3 distinct prime factors?

  • Prime Order
    problem

    Prime Order

    Age
    11 to 14
    Challenge level
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    Weekly Problem 24 - 2006
    How many of the rearrangements of the digits 1, 3 and 5 give prime numbers?

  • flow chart
    problem

    Flow Chart

    Age
    11 to 14
    Challenge level
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    The flow chart requires two numbers, M and N. Select several values for M and try to establish what the flow chart does.

  • Little Goldbach
    problem

    Little Goldbach

    Age
    11 to 14
    Challenge level
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    How many of the numbers 1 to 20 are not the sum of two primes?

  • Great Granddad
    problem

    Great Granddad

    Age
    11 to 14
    Challenge level
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    Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?

  • 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!?

  • Coins
    problem

    Coins

    Age
    11 to 14
    Challenge level
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    A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?

  • HCF Expression
    problem

    HCF Expression

    Age
    11 to 14
    Challenge level
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    Find out which two distinct primes less than $7$ will give the largest highest common factor of these two expressions.