Math Games Involving Prime Factors

Use raisins to teach about prime factorization.

Factoring is like taking a number apart to see its components. For example, the prime factors of 12 are 2, 2 and 3, since 2 X 2 X 3 = 12. You can teach students to factor by making simple factor trees, but adding some competition or high-interest activity can help them be more engaged in learning about factorization.

Build a Factorization Tree

To play this game, divide students into teams and give each team a pile of index cards, toothpicks and several pens. Call out a number and let students work together to make the factorization tree for that number. The numbers in the factorization tree should be made by writing them on the index cards and the toothpicks should connect the numbers together into a tree. The first team to complete the factorization tree correctly wins the round.

Steal the Number

For this active game, you'll need to divide the class into two teams. The two teams stand against opposite walls, in two straight lines. Walk down each line, giving out numbers starting from one. When you finish, there should be one student on each team with any given number. For each round, place two index cards on the floor, each one with a two digit number on it. Call out a number. The student with that number on each team runs forward and tries to pick up the number with the highest amount of factors. (The other player picks up the remaining card.) The teams then figure out how to factor the number to see whether the choosing player was correct. The player who was holding the number with the most factors wins a point for his team.

Using Manipulatives

In this activity, students work in small groups to show what a prime factor actually is. Give the groups boxes of raisins or other small objects. They should also have cups of different sizes to place the raisins in. (The number of cups must always be prime.) Students first divide the raisins evenly among a number of large cups, then divide the raisins in each cup evenly into medium-sized cups, then divide the raisins in the medium cups evenly into small cups. When they finish, they should have a visual representation of factoring. For example, if they are using 60 raisins, they might first divide the raisins into two large cups, with 30 raisins each. They would then put five medium cups into the large cups and divide the raisins evenly so that there were six in each. They would then put three small cups inside the medium cups and place two raisins in each. They would then see that the factorization was 2 (raisins) X 3 (small cups) X 5 (medium cups) X 2 (large cups).

The Largest Prime Factor

Use a factor generator to play this game (see Resource 1). Challenge students to choose large numbers, such as 2,039,492, and compete to see who can come up with a number that has either the largest number of prime factors, or the greatest prime factor. Put the numbers into the generator and see who was right.

References

• Energize the Classroom: Prime Factorization Game

Resources

• Washington University in St. Louis: Find the Prime Factors of a Number (Number Generator)