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The Genie in the Jar
Age 11 to 14
Challenge Level 
Why do this problem?
This problem requires both clear thinking and the use of prime factors. It does not require much knowledge of volume and capacity.Key questions
What are the factors of $595$?
What is its most obvious factor?
Why not try dividing by $5$?
What are the factors of the result of doing this?
Why not call the "numbers" g, o and v?
Does the problem ask which number is which?
Possible extension
Learners could go on to Stars for more work on factors.Possible support
Suggest doing Three Spinners which is a simpler problem involving factors.You may also like
Adding All Nine
Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!
Double Digit
Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. Try lots of examples. What happens? Can you explain it?
Repeaters
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.