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?
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.
To find the greatest number of groups that can be formed, we need to find the highest common factor (HCF) of the number of coaches and players.
The number of coaches is 12, and the number of players is 30.
To find the HCF, we can list the factors of both numbers:
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
From the list, we can see that the highest common factor is 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 need to divide the total number of coaches and players by the number of groups.
Number of coaches per group: 12 / 6 = 2 coaches
Number of players per group: 30 / 6 = 5 players
Therefore, each group will have 2 coaches and 5 players.
To find the greatest number of groups that can be formed, we need to find the highest common factor (HCF) of 12 (number of coaches) and 30 (number of players).
Let's list the factors of 12: 1, 2, 3, 4, 6, 12.
And the factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.
The highest common factor among these numbers is 6. Therefore, the greatest number of groups that can be formed is 6.
To figure out the number of coaches and players in each group, we need to divide the total number of coaches and players by the number of groups.
Total coaches: 12
Total players: 30
Number of groups: 6
Number of coaches in each group: 12 ÷ 6 = 2
Number of players in each group: 30 ÷ 6 = 5
So, the greatest number of groups that can be formed is 6, and each group will consist of 2 coaches and 5 players.