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#14 Factor graphs

Set by Katie Steckles

To construct a factor graph, we dot numbers around a page and draw lines between pairs where one is divisible by the other. Start by writing the numbers 1 and 2, and join them with a line – since 2 is divisible by 1. Then write 3 and join it only to 1 (since 3 is divisible by 1 but not 2). The number 4 would connect to 1 and 2 but not 3, and so on. The connecting lines need not be straight.

Can you continue adding numbers and connecting them to their factors until you have all the numbers from 1 to 10, but without any of the lines crossing anywhere? (You may need to redraw if you get stuck.)

How many more numbers can you add before this becomes impossible?

If you don’t include the number 1 in your graph and instead start from 2, how many numbers can you add without creating lines that cross?

Solution next week

#13 Number Venns

Solution

Here is one set of rules for each diagram – you may find others!

1. A contains multiples of 3 and B contains multiples of 4. The number 24 could also be added to the centre section.

2. A contains prime numbers and B contains even numbers. Nothing else can be added to the intersection, as 2 is the only even prime.

3. A contains triangular numbers (those that can be represented by that many dots arranged in an equilateral triangle, like 3, 6 or 10) and B contains square numbers. The next number that is both square and triangular is 36, which is out of our range of 1-30, so nothing else can be added here.