Divisibility

problem
Differences

Age

11 to 14

Challenge level

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
problem
Square routes

Age

11 to 14

Challenge level

How many four digit square numbers are composed of even numerals? What four digit square numbers can be reversed and become the square of another number?
problem
Expenses

Age

14 to 16

Challenge level

What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?
problem
Legs eleven

Age

11 to 14

Challenge level

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?
problem
Dozens

Age

7 to 14

Challenge level

Can you select the missing digit(s) to find the largest multiple?
problem
Big powers

Age

11 to 16

Challenge level

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.
problem
Oh! Hidden inside?

Age

11 to 14

Challenge level

Find the number which has 8 divisors, such that the product of the divisors is 331776.
problem
Repeaters

Age

11 to 14

Challenge level

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.
problem
Counting factors

Age

11 to 14

Challenge level

Is there an efficient way to work out how many factors a large number has?
problem
Latin numbers

Age

14 to 16

Challenge level

Can you create a Latin Square from multiples of a six digit number?