Math Game Monday: Factors and Multiples

This game blends strategy and factoring practice, challenging players to think several steps ahead.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

Factors and Multiples

Math Concepts: multiplication, division, factors and multiples.

Players: two to four.

Equipment: printed hundred chart, pencils or markers. Calculator optional.

The FREE 68-page printable (pdf) Prealgebra & Geometry Printables file features hundred charts, coordinate grids, assorted graph paper, and all the game boards for the Math You Can Play: Prealgebra & Geometry book.

How to Play

Print a single hundred chart for the players to share.

The first player chooses an even number less than fifty and marks that square on the hundred chart by coloring the square or drawing a large X over the number. Then the next player marks one factor or multiple of that number.

Players alternate turns, each marking an available (unmarked) factor or multiple of the last number played.

The player who takes the last legal number, leaving the other players with no move, wins the game.

Variations

For a shorter game, cross out rows to limit the playable area of the gameboard. Try playing with 1–30 or 1–60.

Factors and Multiples Cooperative Game: Work together to find a long set of factors and multiples. Try to keep the game going, not to block the next player. Keep a list of your numbers in the order you use them. Can you mark more than half of the chart without breaking the chain?

Words to Know

The words factor and multiple always refer to whole numbers, not fractions or decimals. Factors are the numbers you multiply, and multiples are the answers you get. A factor always divides evenly (without remainder) into any of its multiples — so a factor may also be called a divisor of its multiple.

For example, the factors of twelve are 1, 2, 3, 4, 6, and 12, because those are all the whole numbers you can multiply to get twelve:
1 × 12 = 12
2 × 6 = 12
3 × 4 = 12
And twelve is a multiple of each of its factors.

History (and a Puzzle)

Factors and Multiples comes from the Nrich Maths website, a great place to visit and explore. You’ll find an amazing variety of mathematical puzzles, games, and challenge problems for all ages.

Puzzle: Why is there a restriction on the first number marked? Try playing a two-player game without that rule and see what happens. Can you figure out a strategy for the first player to guarantee a win?