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NRICH: Factors and Multiples Game
##### This is a game for two players.

The first player chooses a positive even number that is less than 50, and crosses it out on the grid.

The second player chooses a number to cross out. The number must be a factor or multiple of the first number.

Players continue to take it in turns to cross out numbers, at each stage choosing a number that is a factor or multiple of the number just crossed out by the other player.

The first person who is unable to cross out a number loses.

Play a few times to get a feel for the game.

Do you have any winning strategies?

Here is an interactive version of the game in which you drag the numbers from the left hand grid and drop them on the right hand grid. Alternatively, click on a number in the left hand grid and it will transport to the earliest empty location in the right hand grid. You can rearrange the numbers in the right hand grid by dragging and dropping them in position. The integer in the top right hand corner grows with the number of factors/multiples you have in a row.

Alternatively, you can print out some 1-100 square grids.
Now for a collaborative challenge…
Rather than playing against a partner, it’s time to work together with them to find the longest sequence of numbers that can be crossed out.
Can you cross out more than half the numbers? How are you approaching this challenge to try and make your sequence as long as possible?
You might find this sheet useful, which includes the instructions for this collaborative task with a 100 square.

Printable NRICH Roadshow resources: Instructions + Grid in 2 parts here and here.

##### Age 7 to 16

Multiplication & Division
K-6, Middle School, High School

## Organization

NRICH (University of Cambridge)

Online Game