Multiplication and division

You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by 3, 5 and by 7...

6! = 6 × 5 × 4 × 3 × 2 × 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4) = 45. What is the highest power of two that divides exactly into 100!?

Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain why this works.

Can you reconstruct the long division calculation from the 'skeleton'?

Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?

How many zeros are there at the end of the number which is the product of first hundred positive integers?

Can you produce convincing arguments that a selection of statements about numbers are true?

Vedic Sutra is one of many ancient Indian sutras which involves a cross subtraction method. Can you give a good explanation of WHY it works?