### Why do this problem?

This problem involves calculating with fractions and also uses knowledge of factors and multiples. It is a difficult problem that requires clear and logical thinking.

### Key questions

How do you think you can start on this problem?
Would it help to make a list of some prime numbers?
Why not think of numbers which have many factors and try them?
Would it help to make a list of numbers which have many factors?
Why not start with $12$? What are its factors?
Are all the numbers up to $12$ either a prime number or a fraction that will simplify?
Now do you think you can try with larger numbers?

### Possible extension

Learners could on to Peaches Today, Peaches Tomorrow.

### Possible support

If learners are finding coping with fractions are very difficult suggest trying this Stage 2 problem, Fractions Made Faster or even Fractional Wall.