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### Number and algebra

### Geometry and measure

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### Working mathematically

### For younger learners

### Advanced mathematics

# Factors and Multiples Game

#### Tablet version Install in home page

**Now for a collaborative challenge...**
*You might find this sheet useful, which includes the instructions for this collaborative task with a 100 square.*

**You may now enjoy having a go at Xavi's T-shirt.**

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### Pebbles

### Bracelets

### Sweets in a Box

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

Or search by topic

*Factors and Multiples printable worksheet - game
Factors and Multiples printable worksheet - puzzle
On this resources page there are printable 1-100 square grids.*

**You may like to have a go at Dozens before having a go at this challenge. **

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.

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?**

*This activity featured in an NRICH video in June 2020 and an NRICH student webinar in November 2020.*

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?