Factors, Multiples and Primes Short Problems: Age 11-16

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Factors, Multiples and Primes: Age 11-16.

We have put together a selection of these short problems as printable worksheets:

Printable worksheets: Age 11-14 ⭐   Printable worksheets: Age 11-14 ⭐⭐   Printable worksheets: Age 11-14 ⭐⭐⭐

Printable worksheet: Age 14-16 ⭐   Printable worksheets: Age 14-16 ⭐⭐   Printable worksheets: Age 14-16 ⭐⭐⭐   Printable worksheet solutions


  • Small tomato seedlings in pink pots.
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    Eight Factors Only

    Age
    14 to 16
    Challenge level

    We are given two factors of a number with eight factors. Can you work out the other factors of the number?

  • Small tomato seedlings in pink pots.
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    Rational Integer

    Age
    14 to 16
    Challenge level

    Weekly Problem 39 - 2012
    For how many values of $n$ are both $n$ and $\frac{n+3}{n-1}$ integers?

  • Small tomato seedlings in pink pots.
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    Integer Indices

    Age
    14 to 16
    Challenge level

    From this sum of powers, can you find the sum of the indices?

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    Leftovers

    Age
    14 to 16
    Challenge level

    Weekly Problem 26 - 2008
    If $n$ is a positive integer, how many different values for the remainder are obtained when $n^2$ is divided by $n+4$?

  • Small tomato seedlings in pink pots.
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    Three Primes

    Age
    14 to 16
    Challenge level

    Weekly Problem 6 - 2010
    Can you find three primes such that their product is exactly five times their sum? Do you think you have found all possibilities?

  • Small tomato seedlings in pink pots.
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    Square LCM

    Age
    14 to 16
    Challenge level

    Using the hcf and lcf of the numerators, can you deduce which of these fractions are square numbers?

  • Small tomato seedlings in pink pots.
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    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?

  • Small tomato seedlings in pink pots.
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    Factor List

    Age
    14 to 16
    Challenge level

    Tina has chosen a number and has noticed something about its factors. What number could she have chosen? Are there multiple possibilities?

  • Small tomato seedlings in pink pots.
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    Square Product

    Age
    14 to 16
    Challenge level

    Weekly Problem 10 - 2011
    Will this product give a perfect square?

  • Small tomato seedlings in pink pots.
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    Super Computer

    Age
    14 to 16
    Challenge level

    What is the units digit of the given expression?

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    Primes and Six

    Age
    14 to 16
    Challenge level

    Weekly Problem 1 - 2015
    If $p$ and $q$ are prime numbers greater than $3$ and $q=p+2$, prove that $pq+1$ is divisible by $36$.

  • Small tomato seedlings in pink pots.
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    Adding a Square to a Cube

    Age
    14 to 16
    Challenge level

    If you take a number and add its square to its cube, how often will you get a perfect square?

  • Small tomato seedlings in pink pots.
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    Cancelling Fractions

    Age
    14 to 16
    Challenge level

    Can you find a fraction with the following properties?

  • Small tomato seedlings in pink pots.
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    Fortunate Inflation

    Age
    14 to 16
    Challenge level

    The price of an item in pounds and pence is increased by 4%. The new price is an integer number of pounds. Can you find it?

  • Small tomato seedlings in pink pots.
    problem

    Obviously?

    Age
    14 to 18
    Challenge level

    Find the values of n for which 1^n + 8^n - 3^n - 6^n is divisible by 6.

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