1. Benny is setting up fish tanks at the pet store. He has 8
angel fish, 12 tiger barbs , and 24 guppies. If he wants to
have the same number of each kind of fish in every tank,
what is the greatest number of tanks he can set up?
What is the greatest common factor?
To find the greatest number of tanks Benny can set up, we need to determine the greatest common divisor (GCD) of the quantities of each type of fish.
Let's list the quantities of each type of fish:
- Angel fish: 8
- Tiger barbs: 12
- Guppies: 24
To find the GCD, we can use the method of prime factorization. Let's break down each quantity into its prime factors:
For angel fish:
- 8 = 2 × 2 × 2
For tiger barbs:
- 12 = 2 × 2 × 3
For guppies:
- 24 = 2 × 2 × 2 × 3
Now, let's identify the common prime factors among the three quantities:
- The common prime factors are 2 and 2.
Finally, we find the GCD by multiplying the common prime factors:
- GCD = 2 × 2 = 4
Therefore, Benny can set up a maximum of 4 tanks with the same number of each kind of fish.