## CHAPTER 1: NUMBER RELATIONSHIPS

**Lesson 7: Determining Common Factors **

**Goal**

Determine factors, common factors, and the greatest common factor of whole numbers.

**Instructions for Use**

**Factor Game**

To use Factor Game, click on “Instructions” and read them carefully. Note that you can either play against another player or against the computer by selecting the appropriate choice in the box at the lower left. Scores are kept automatically based on the total of the numbers selected for your opponent to factor and on the sum of the factors you identify for the numbers your opponent selects. You can vary the difficulty of the game by selecting either30, 49, or 100 in the “Game Type” box below the grid.

**Factor Tree**

To use Factor Tree, consider what number could be a factor of the least common multiple (LCM) shown in the yellow box near the top of the screen. Type your number in the blank white box below and hit “Enter”. If your number is a factor, the other factor of the LCM will appear in the box to its right. If either of these factors is a multiple of other factors a new pair of boxes to be filled in will appear below. If a number you type is not a factor an error message will appear and you will need to correct your number. When all the factors have been found they are displayed at the bottom of the screen. You can then click on “New Problem” to play again. To vary the game you can also choose between “One” and “Two” trees and between “Computer” and “User” generated numbers by clicking on the respective buttons at the bottom. At the end of two tree games, common and other factors can be shown in a Venn diagram.

**CGF**

To use GCF, read the definition and method by which to find the GCF. Then scroll down to “Practice” and click on “Start”. A pair of numbers will display in the box below this button as a timer counts elapsed time in the “Report Totals” box. Enter your GCF in the box to the right and click “check”. If your answer is correct a new pair of numbers will be displayed. If not, an error box will display the correct answer. Click “Ok” to resume play. You can also vary the game by scrolling down to “Play” and clicking on one of the choices shown in the 3 yellow boxes at left.