Factors and multiples

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

What could be the scores from five throws of this dice?

Each time a class lines up in different sized groups, a different number of people are left over. How large can the class be?

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

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

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

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

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

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?