The coach of a baseball team separates the players into groups for drills. Each group has the same number of players. Is the total number of players on baseball team prime or composite? Explain.
It is divisible by 2
To determine if the total number of players on a baseball team is prime or composite, we need to understand the concept of prime and composite numbers.
A prime number is a whole number greater than 1 that has no positive divisors other than 1 and itself. For example, 2, 3, 5, 7, 11, and 13 are all prime numbers.
A composite number is a whole number greater than 1 that is divisible by more than just 1 and itself. In other words, it has at least one positive divisor other than 1 and itself. For example, 4, 6, 8, 9, and 12 are all composite numbers.
Now let's apply this understanding to the total number of players on a baseball team. We are told that the coach separates the players into groups for drills, and each group has the same number of players.
If the total number of players on the team is a prime number, it means there are no possible equal group sizes since prime numbers only have two divisors, 1 and itself. In this case, the coach would not be able to make equal groups.
However, if the total number of players is a composite number, it means there are multiple possible ways to divide the players into equal groups, assuming the coach wants each group to have the same number of players. For example, if the total number of players is 12, the coach could form groups of 2, 3, 4, or 6 players.
Therefore, if the coach can create equal groups for drills, the total number of players on the baseball team must be a composite number.