Question

analyze and persevere the venn diagram at the right shows the factors of 24 and 40.
a. what is the meaning of each of the three shaded regions?
b. explain how you can use the venn diagram to find the gcf of 24 and 40. what is the gcf of 24 and 40?

Explanation:

Step1: Analyze the Venn diagram regions

• The left - hand circle (orange) represents the factors of 24. The numbers \(3,6,12,24\) are factors of 24 but not of 40.
• The overlapping region (green) represents the common factors of 24 and 40. The numbers \(1,2,4,8\) are factors of both 24 and 40.
• The right - hand circle (blue) represents the factors of 40. The numbers \(5,10,20,40\) are factors of 40 but not of 24.

Step2: Use the Venn diagram to find the GCF

The greatest common factor (GCF) is the largest number in the overlapping region of the Venn diagram. Looking at the overlapping region (green) with numbers \(1,2,4,8\), the largest number is 8.

Answer:

a. The orange region: factors of 24 only; the green region: common factors of 24 and 40; the blue region: factors of 40 only.
b. The GCF is the largest number in the overlapping region. The GCF of 24 and 40 is 8.