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'Factor Track' printed from https://nrich.maths.org/

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Factor Track printable sheet

Factor Track is not a race but a game of skill.
Below is a simple training version. The idea is to go round the track in as few turns as possible, keeping to the rules.

A track of numbers

For accessibility, clicking on the 'show' button below will show a description of this image.

The track consists of straight lines of squares that are either blank or have numbers in. The straight lines of squares are joined by corner squares.

Start: 60

Blank

14

48

25

40

31

10

19

Corner: 28

Blank

72

2

24

Blank

9

Corner: 18

Blank

13

Corner: 14

Blank

Corner: 24

Blank

3

Corner: 36

Blank

7

Corner: 32

Blank

Blank

5

Corner: 14

Blank

2

7

10

6

19

End

Rules:
You start on the 'Start' square and must make your way round to the 'End' square.
You can move any factor of the number you are on, except 1.
You must land exactly on each corner (green) square, so you can't go round corners in one turn.
 
Have a go at moving round this 'training' track following the rules.  
Can you do it in fewer turns?

When you feel ready, try this more complicated track where there are possible short cuts. You will have to work out whether they are worthwhile. You can click on this image to make it bigger.

A track of numbers

For accessibility, clicking on the 'show' button below will show a description of this image.

The track consists of straight lines of squares that are either blank or have numbers in. The straight lines of squares are joined by corner squares.

Start: 60

Blank

14

48

25

10

45

31

19

Corner: 28

Blank

72

2

Three-way corner A: 36

Blank

46

15

28

23

Corner: 56

Blank

55

28

13

43

42

Corner: 30

Blank

11

15

27

8

Corner: 24

Blank

7

39

4

17

Corner: 28

Blank

8

9

Corner: 48

Blank

Three-way corner B: 20

Blank

4

13

Corner: 27

Blank

31

Corner: 36

Blank

Corner: 20

Blank

16

2

41

Corner: 32

Blank

8

19

Three-way corner C: 4

Alternate route from B to C:

Three-way corner B: 20

Blank

Corner: 98

Blank

Corner: 76

Blank

67

21

Three-way corner C: 4

Blank

Corner: 40

Blank

16

23

Corner: 12

Blank

56

Three-way corner D: 49

Alternate route from A to D:

Three-way corner A: 36

Blank

9

Corner: 51

Blank

13

Corner: 96

Blank

23

19

Corner: 81

Blank

3

Corner: 54

Blank

87

11

7

Corner: 72

Blank

14

5

Three-way corner D: 49

Blank

7

2

10

6

19

End


You might find it easier to print out this larger copy of the track which also has the rules on it.

You can do this on your own or with a friend. Who can get round in the least number of turns?

What is the best route to take to do it in the least number of turns?
Which squares do you need to land on?

Printable NRICH Roadshow resource.