Football tryouts at a local school, 12 coaches and 30 players will split into groups. Each group will have the same number of coaches and players. What is the greatest number of groups that can be formed? How many coaches and players will be in each of these groups?

Answer 1

In order to find the greatest number of groups that can be formed, we need to find the greatest common divisor (GCD) of the number of coaches and players.

The factors of 12 are 1, 2, 3, 4, 6, and 12.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.

The common factors are 1, 2, 3, and 6.

Therefore, the greatest number of groups that can be formed is 6.

To find the number of coaches and players in each group, we divide the total number of coaches and players by the number of groups.

Number of coaches in each group = 12 / 6 = 2 coaches
Number of players in each group = 30 / 6 = 5 players

Therefore, each group will have 2 coaches and 5 players.