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.
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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