Growing Garlic

Ben is on the allotment with his Mum. They would like to grow some garlic and are deciding how to plant the garlic cloves.

Ben arranges the cloves into three equal rows and finds that he has one spare clove.
How many cloves might he have had to start with?
How do you know?

Ben plants cloves of garlic in two equal rows and has one clove left over. So he tries again.
He plants cloves in three equal rows and has one left over. So he tries again.
He plants cloves in four equal rows and has one left over. So he tries again.
He plants cloves in five equal rows and has one left over. So he tries again.
He plants cloves in six equal rows and still has one left over.
We know that he has fewer than 100 garlic cloves. How many did he have?
How do you know?

How many cloves might he have had if there were more than 100?

You might like to use this interactivity to try out your ideas: