Starting with a 100 Grid, the first player chooses a positive even number that is less than 50, and crosses it out on the grid. The second player chooses a number to cross out. The number must be a factor or multiple of the first number.

Players continue to take it in turns to cross out numbers, at each stage choosing a number that is a factor or multiple of the number just crossed out by the other player. The first person who is unable to cross out a number loses.

http://nrich.maths.org/public/viewer.php?obj_id=5468

Students practice their knowledge of factors and products. There are links to lessons on how you might use this engaging game in the classroom.
http://illuminations.nctm.org/ActivityDetail.aspx?ID=29

The factor game is a classic! Play against a friend or play against the computer. All you need to win is a good knowledge of factors and a bit of logic to figure out a winning stragegy!
http://illuminations.nctm.org/ActivityDetail.aspx?ID=12

This manipulative allows you to construct factor trees (to the prime factors) for two numbers, and then from the prime factorization, you are asked to identify the Least Common Multiple (LCM) and the Greatest Common Factor (GCF) of the two given numbers.
http://nlvm.usu.edu/en/nav/frames_asid_202_g_3_t_1.html?open=instruction...

This virtual manipulative displays a number grid containing numbers from 2 to 200. You can use it to explore patterns and relationships involving multiples.
http://nlvm.usu.edu/en/nav/frames_asid_158_g_1_t_1.html?open=instruction...

You are playing snooker on an m x n snooker table with 4 corner pockets. You always start at a corner and hit the ball at a 45 degree angle. Which pocket will the ball land in? Do the values of m and n matter? Investigate!
http://www.subtangent.com/maths/ig-snooker.php