In this game players take turns choosing a starting value from a set of available numbers, and then alternately factorise until it is fully decomposed into its prime factors. Players score the number of points given by each number chosen or factor entered. However, there is a catch. Since factors occur as pairs, although the choosing player scores the value chosen, their opponent scores points according to the other factor in the pair. So, for example, it is not only important to recognise that 5 is a factor of 95: for best play a player must calculate 19 as the other factor, and so score 19 points while only giving 5 away.

Hit the Setup… button to configure play — as two players or teams, or compete against the computer. Play continues until all values have been fully factorised, and the winner is the player with most points.


Factor Champion
Who will be the Factor Champion?

  • Hit the Setup… button to configure play.
  • Players take turns to choose a starting value from the set of available numbers, and then alternately click on the factor tree to further factorise any composite numbers.
  • For all starting numbers and factors chosen, that number of points are scored by the choosing player.
  • However, for each factor chosen, the other player scores a number of points equal to the other factor. For example, if the number is 10 and Player 1 chooses 5 for the factor, the other player will score 2 since 10 = 5 × 2.
  • Only proper factors are permitted — that is positive values greater than 1 and less than the value. If you enter an invalid number, you lose your turn!
  • Play continues until all values have been fully factorised.
Player 1:
Player 2:
Or click here to play against the computer.

Select Game Speed:  Slow   Medium   Fast 

Numbers:

Choose a number…

 

About the activity

This activity is designed to promote fun and competitive factor finding, all the way to the complete prime factorisation. The display of factors as the game proceeds allows the results to be explored during play. Since each factorisation involves both players scoring points, the game naturally rewards players who think about both values in a factorisation, as well as all possible factors.

Choose a random collection of numbers for a more challenging activity.