Question

gary is forming capture the flag teams out of all of the students that signed up from two classes. each team must have the same number of players and be from the same class. what is the largest number of players that gary can put on each team?

	class a	class b

option 1:
30 → 2 × 3 × 5
24 → 2 × 2 × 2 × 3
gcf = 2 + 3
team size = 5

option 2:
30 → 2 × 3 × 5
24 → 2 × 2 × 2 × 3
gcf = 5 × 2 × 2
team size = 20

option 3:
30 → 2 × 3 × 5
24 → 2 × 2 × 2 × 3
gcf = 2 × 2 × 2 × 3 × 5
team size = 120

option 4:
30 → 2 × 3 × 5
24 → 2 × 2 × 2 × 3
gcf = 2 × 3
team size = 6

Explanation:

Step1: Find GCF of 24 and 30

Prime factorize 24: \(24 = 2\times2\times2\times3\)
Prime factorize 30: \(30 = 2\times3\times5\)

Step2: Identify common factors

Common prime factors are 2 and 3.

Step3: Calculate GCF

Multiply common factors: \(GCF = 2\times3 = 6\)

Answer:

The correct option is the one with \(GCF = 2\times3\) and Team Size = 6 (the bottom - right option in the given choices).