knowing powers of 2

This is a list of powers of 2. You may scroll down (or use arrow keys) to see more down the list.

Here are some questions or tasks we may set with this list of powers.

Pick any two red numbers and multiply them. Is the product also on the list?
I pick two red numbers and multiply, then get 2048. Which could be the two numbers?
I divide one red number by another one, then get 32. Which could be the two numbers?
If you multiply each red number by 2 and put the result in column D, what pattern do you notice?
If you square each red number by 2 and put the result in column D, what pattern do you notice?
If you divide each red number by the one above it and put the result in column D, what would you see?
If you subtract each red number from the one below it and put the result in column D, what would you see?

Do you have any suggestion of questions and tasks? This activity is developed based on ideas from an earlier package of CDI in Hong Kong: https://www.evernote.com/l/AAOhCHkfAbpHGJxN1BO4JylCYChX0Yc-p9E

How the table is formed:

Thanks to Anthony Or for this formatting method. It is actually better to copy and paste with Latex formatting in classic 5.