Final answer:
A Venn diagram can display the factors of two numbers and their common factors by listing each number's factors in separate circles with the overlapping area revealing shared factors. For instance, for the numbers 36 and 48, the common factors are 1, 2, 3, 4, 6, and 12. Repeat this process for any pair of numbers to visualize and determine their common factors.
Step-by-step explanation:
Venn diagrams are useful for illustrating the common and unique factors between two numbers. To use a Venn diagram for factoring, you'll draw two overlapping circles. Each circle represents the set of factors for one of the two numbers in question. The overlapping area shows the common factors.
Example: Factors of 36 and 48
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Common factors in the overlapping area: 1, 2, 3, 4, 6, 12
These steps can be similarly applied for finding the factors of 16 and 56, 30 and 75, and 54 and 90. You list the factors for each number, place them in the appropriate areas of the diagram, and note which factors are shared.
Example: Factors of 54 and 90
- Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
- Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Common factors in the overlapping area: 1, 2, 3, 6, 9, 18
For each pair of numbers like 16 and 56 or 30 and 75, you would follow this same process to visually represent the factors and identify common factors.