if marching bands vary from 21 to 49 players, which number of players can be arranged in the greatest number of rectangles?
48. You cant arrange 49 into a rectangle.
To find out which number of players can be arranged in the greatest number of rectangles, we need to consider the factors of each number within the given range.
Let's calculate the factors for each number of players within the range of 21 to 49:
For 21: Factors are 1, 3, 7, 21.
For 22: Factors are 1, 2, 11, 22.
For 23: Factors are 1, 23.
For 24: Factors are 1, 2, 3, 4, 6, 8, 12, 24.
For 25: Factors are 1, 5, 25.
For 26: Factors are 1, 2, 13, 26.
For 27: Factors are 1, 3, 9, 27.
For 28: Factors are 1, 2, 4, 7, 14, 28.
For 29: Factors are 1, 29.
For 30: Factors are 1, 2, 3, 5, 6, 10, 15, 30.
For 31: Factors are 1, 31.
For 32: Factors are 1, 2, 4, 8, 16, 32.
For 33: Factors are 1, 3, 11, 33.
For 34: Factors are 1, 2, 17, 34.
For 35: Factors are 1, 5, 7, 35.
For 36: Factors are 1, 2, 3, 4, 6, 9, 12, 18, 36.
For 37: Factors are 1, 37.
For 38: Factors are 1, 2, 19, 38.
For 39: Factors are 1, 3, 13, 39.
For 40: Factors are 1, 2, 4, 5, 8, 10, 20, 40.
For 41: Factors are 1, 41.
For 42: Factors are 1, 2, 3, 6, 7, 14, 21, 42.
For 43: Factors are 1, 43.
For 44: Factors are 1, 2, 4, 11, 22, 44.
For 45: Factors are 1, 3, 5, 9, 15, 45.
For 46: Factors are 1, 2, 23, 46.
For 47: Factors are 1, 47.
For 48: Factors are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
For 49: Factors are 1, 7, 49.
Now, let's count the number of factors for each number of players within the range:
For 21: 4 factors.
For 22: 4 factors.
For 23: 2 factors.
For 24: 8 factors.
For 25: 2 factors.
For 26: 4 factors.
For 27: 4 factors.
For 28: 6 factors.
For 29: 2 factors.
For 30: 8 factors.
For 31: 2 factors.
For 32: 6 factors.
For 33: 4 factors.
For 34: 4 factors.
For 35: 4 factors.
For 36: 9 factors.
For 37: 2 factors.
For 38: 4 factors.
For 39: 4 factors.
For 40: 8 factors.
For 41: 2 factors.
For 42: 8 factors.
For 43: 2 factors.
For 44: 6 factors.
For 45: 6 factors.
For 46: 4 factors.
For 47: 2 factors.
For 48: 10 factors.
For 49: 3 factors.
Based on the calculations, we can see that the number of players with the greatest number of factors is 48. Therefore, 48 players can be arranged in the greatest number of rectangles.