Curious Number

            

Are you curious about numbers? Can you use your mathematical skills to find some solutions to the problems below?

Can you order the digits 1, 2 and 3 to make a number which is divisible by 3?
And when the final digit is removed again it becomes a two-digit number divisible by 2,
then finally a one-digit number divisible by 1?  

Can you order the digits 1, 2, 3 and 4 to make a number which is divisible by 4?
And when the final digit is removed it becomes a three-digit number which is divisible by 3.
And when the final digit is removed again it becomes a two-digit number divisible by 2,
then finally a one-digit number divisible by 1?

Can you order the digits 1, 2, 3, 4 and 5 to make a number which is divisible by 5?
And when the final digit is removed it becomes a four-digit number which is divisible by 4.
And when the final digit is removed it becomes a three-digit number which is divisible by 3.
And when the final digit is removed again it becomes a two-digit number divisible by 2,
then finally a one-digit number divisible by 1?

What systems are you using?
What do you know about numbers which can be divided by 3, 4, 5?
Now what about taking this further for digits 1, 2, 3, 4, 5, and 6?
What do you know about numbers which can be divided by 6, 7, 8 and 9?

You might now like to have a go at the problem Dozens.