Question

1. model with math 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 use the venn diagram to find the gcf of 24 and 40. what is the gcf of 24 and 40?

Explanation:

a.

• The orange - shaded region (only in the circle labeled 24): These are the factors that are unique to 24. That is, numbers that divide 24 but do not divide 40.
• The green - shaded region (the intersection of the two circles): These are the common factors of 24 and 40. Numbers that divide both 24 and 40.
• The blue - shaded region (only in the circle labeled 40): These are the factors that are unique to 40. That is, numbers that divide 40 but do not divide 24.

The greatest common factor (GCF) of two numbers is the largest number that divides both of them. In a Venn diagram of factors, the GCF is the largest number in the intersection (common) region. Looking at the intersection (green) region of the Venn diagram for 24 and 40, the numbers in the intersection are 1, 2, 4, 8. The largest of these numbers is 8.

Answer:

• Orange region: Factors of 24 only. Green region: Common factors of 24 and 40. Blue region: Factors of 40 only.

b.