Name : Shiling
Who is asking the question : Student

I've got this perplexing problem up my hands and I hope that you can solve it.

Here is it : A number can be divided by 16 if its 1st four digits can be divided by 16. How can you prove that?

Grateful for help,
Shiling

There is a similar result concerning divisibility by 4 that should help with your problem concerning divisibility by 16. The result is:

By the "last two digits" I mean the tens and units digits.

Suppose k is an integer with tens digit q and units digit r, then the number can be written

where p is some integer. But 4 divides 100 and hence 4 divides k if and only is 4 divided 10q + r.