Factors and multiples

problem
Sticky fingers

Age

14 to 16

Challenge level

Ruth wants to puts stickers on the cuboid she has made from little cubes. Will she have any stickers left over?
problem
Adjacent factors

Age

11 to 14

Challenge level

Two numbers can be placed adjacent if one of them divides the other. Using only $1,...,10$, can you write the longest such list?
problem
Factor list

Age

14 to 16

Challenge level

Tina has chosen a number and has noticed something about its factors. What number could she have chosen? Are there multiple possibilities?
problem
Product 100

Age

11 to 14

Challenge level

The product of four different positive integers is 100. What is the sum of these four integers?
problem
Light the lights

Age

5 to 7

Challenge level

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
problem
Light the lights again

Age

7 to 11

Challenge level

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you work out the rule for each light?
problem
Gran, how old are you?

Age

7 to 11

Challenge level

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
problem
Charlie's delightful machine

Age

11 to 16

Challenge level

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
problem
Four coloured lights

Age

11 to 14

Challenge level

Imagine a machine with four coloured lights which respond to different rules. Can you find the smallest possible number which will make all four colours light up?
problem
Our numbers

Age

5 to 7

Challenge level

These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?