Factors and multiples

Are these domino games fair? Can you explain why or why not?

Weekly Problem 48 - 2013
What is the remainder when the number 743589×301647 is divided by 5?

Which of the numbers shown is the product of exactly 3 distinct prime factors?

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

Can you work out what step size to take to ensure you visit all the dots on the circle?

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

Can you place the numbers from 1 to 10 in the grid?

Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?