How Do I Use a Venn Diagram to Factorize Numbers?

A Venn diagram is used in math to show relationships.

Factoring, or factorizing, numbers is when you find all the numbers that can be multiplies to get another number. For example, the factors of 21 are 3 and 7, because 3 x 7 = 21. A Venn diagram is a graphical tool that shows a relationship between items. A Venn diagram is usually displayed as a series of overlapping circles. The circles display the items, and the overlapping areas are what the items have in common. A Venn diagram is an ideal way to show what factors two or more numbers have in common.

Things You'll Need

• Paper
• Pencil

Instructions

1. Draw a circle on a piece of paper.

2. Draw a second circle the same size as the first circle. Overlap the two circles by a quarter.

3. Write one number you want to factor above the left-hand circle. For example, write "24" above the circle.

4. Write the second number you are trying to factor above the right hand circle. For example, write "36" above the right-hand circle.

5. Write all of the factors of 24 inside the circle labeled "24" and write all of the factors for 36 inside the circle labeled "36." Factors are numbers that when multiplied together with another factor equal the number. For example, 24 x 1 = 24, so two factors of 24 are 24 and 1. The factors of 24 are 1,2,3,4,6,8,12 and 24 and the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. Leave the intersection of the two circles blank.

6. Place the common factors inside the intersection of the two circles. In the above example, write "1, 2, 3, 4 and 6" as the common factors.

Tips & Warnings

• If you are comparing three numbers, lay the three circles out in an equilateral triangle with each circle slightly overlapping the other two circles. Use the very central space for factors in common with all three circles.

References

• Learner: Multiples and Factors
• University of Northern Iowa: Venn Diagrams