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Gabriel's Problem and Counting Factors might be good problems to try before looking at this one.

If you know the prime factors of a number, how can you work out which two-digit numbers are factors?

It might help to draw a factor tree.

If you'd like some help with the extension, click below

What is the largest that the four-digit number can be?
What is the smallest that the two-digit number can be?
What does this tell you about the three-digit number?

Now it might be helpful to think about the units digits.