Answered

Coach Smith has three teams of dancers. The first team has 32 members. The second team has 48 members. The third team has 64 members.

Coach Smith wants to divide each team into smaller groups so that each group in each team has the same number of members and there are no members left over.

What is the maximum number of members that he can put into each group?



Answer :

GinnyAnswer

Final answer:

To determine the maximum number of members in each group for Coach Smith's dance teams, find the greatest common divisor (GCD) of the team sizes, which is 16.


Explanation:

To find the maximum number of members in each group for each team, we need to determine the greatest common divisor (GCD) of the team sizes.

For the first team with 32 members, the factors are 1, 2, 4, 8, 16, 32. For the second team with 48 members, the factors are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. Lastly, for the third team with 64 members, the factors are 1, 2, 4, 8, 16, 32, 64.

The largest number that divides all three team sizes without any remainder is the maximum number of members per group.

From the factors, we can see that the greatest common divisor (GCD) of 32, 48, and 64 is 16. Therefore, Coach Smith can put a maximum of 16 members into each group for all three teams.


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