Factors and multiples

problem
Factorial

Age

14 to 16

Challenge level

How many zeros are there at the end of the number which is the product of first hundred positive integers?
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
Expenses

Age

14 to 16

Challenge level

What is the largest number which, when divided into these five numbers in turn, leaves the same remainder each time?
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
Hypotenuse lattice points

Age

14 to 16

Challenge level

The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?
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?