Gabby has 130 insects in her bug collection that have wings and 70 that have pincers. She wants to buy a display case for her collection, but is unsure how many she will need. Each display case should have an equal number of insects with wings and pincers. How many display cases does she need to buy?

What is the greatest common factor of 130 and 70?

10 70: 2 5 7

130: 2 5 13
GCF: 2 5
The Greatest Common Factor (GCF) is: 2 x 5 = 10
Hoped it helped!

Right. She needs 10 cases.

Thanks

You're welcome, Amy.

To determine the number of display cases Gabby needs to buy, we need to find the common factor of the number of insects with wings (130) and the number of insects with pincers (70).

Let's find the factors of 130 first:
Factors of 130: 1, 2, 5, 10, 13, 26, 65, 130

Next, let's find the factors of 70:
Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70

From both lists, we see that the common factors of 130 and 70 are 1, 2, 5, and 10.

Since Gabby wants an equal number of insects with wings and pincers in each display case, the common factor we are interested in is 10, as it allows for an equal distribution of both types of insects.

Therefore, Gabby needs to buy a total of 10 display cases.